Maths-
General
Easy

Question

∫ [1 + tan x α tan (x + α)] dx is equal to -

  1. cot α. log open vertical bar fraction numerator sin invisible function application x over denominator sin invisible function application left parenthesis x plus alpha right parenthesis end fraction close vertical bar plus C    
  2. tan α . log open vertical bar fraction numerator sin invisible function application x over denominator sin invisible function application left parenthesis x plus alpha right parenthesis end fraction close vertical bar plus C    
  3. cot α . log open vertical bar fraction numerator cos invisible function application x over denominator cos invisible function application left parenthesis x plus alpha right parenthesis end fraction close vertical bar plus C    
  4. none of these    

The correct answer is: cot α . log open vertical bar fraction numerator cos invisible function application x over denominator cos invisible function application left parenthesis x plus alpha right parenthesis end fraction close vertical bar plus C


    not stretchy integral open curly brackets 1 plus fraction numerator sin invisible function application x sin invisible function application left parenthesis x plus alpha right parenthesis over denominator cos invisible function application x times cos invisible function application left parenthesis x plus alpha right parenthesis end fraction close curly bracketsdx
    = not stretchy integral open square brackets fraction numerator cos invisible function application x cos invisible function application left parenthesis x plus alpha right parenthesis plus sin invisible function application x sin invisible function application left parenthesis x plus alpha right parenthesis over denominator cos invisible function application x. cos invisible function application left parenthesis x plus alpha right parenthesis end fraction close square brackets d x
    = not stretchy integral fraction numerator cos invisible function application left parenthesis x plus alpha minus x right parenthesis over denominator cos invisible function application x. cos invisible function application left parenthesis x plus alpha right parenthesis end fraction d x
    = cos invisible function application alpha not stretchy integral fraction numerator d x over denominator cos invisible function application x. cos invisible function application left parenthesis x plus alpha right parenthesis end fraction
    Multiply denominator and numerator by sin 
    = fraction numerator cos invisible function application alpha over denominator sin invisible function application alpha end fraction not stretchy integral fraction numerator sin invisible function application alpha over denominator cos invisible function application x. cos invisible function application left parenthesis x plus alpha right parenthesis end fraction d x
    = cot invisible function application alpha not stretchy integral fraction numerator sin invisible function application left parenthesis x plus alpha minus x right parenthesis over denominator cos invisible function application x. cos invisible function application left parenthesis x plus alpha right parenthesis end fraction d x
    = cot invisible function application alpha not stretchy integral fraction numerator sin invisible function application left parenthesis x plus alpha right parenthesis cos invisible function application x minus cos invisible function application left parenthesis x plus alpha right parenthesis sin invisible function application x over denominator cos invisible function application x. cos invisible function application left parenthesis x plus alpha right parenthesis end fraction d x
    = cot invisible function application alpha not stretchy integral left curly bracket tan invisible function application left parenthesis x plus alpha right parenthesis minus tan invisible function application x right curly bracket d x
    = cot invisible function application alpha open square brackets log invisible function application vertical line sec invisible function application left parenthesis x plus alpha right parenthesis vertical line minus log invisible function application vertical line sec invisible function application x vertical line close square brackets plus C
    = cot invisible function application alpha log invisible function application open vertical bar fraction numerator sec invisible function application left parenthesis x plus alpha right parenthesis over denominator sec invisible function application x end fraction close vertical bar plus C
    = cot invisible function application alpha log invisible function application open vertical bar fraction numerator cos invisible function application x over denominator cos invisible function application left parenthesis x plus alpha right parenthesis end fraction close vertical bar plus C

    Related Questions to study

    General
    physics-

    A sound wave of wavelength 32 cm enters the tube at S as shown in the figure. Then the smallest radius r so that a minimum of sound is heard at detector D is

    A sound wave of wavelength 32 cm enters the tube at S as shown in the figure. Then the smallest radius r so that a minimum of sound is heard at detector D is

    physics-General
    General
    physics-

    The rope shown at an instant is carrying a wave travelling towards right, created by a source vibrating at a frequency n. Consider the following statements

    I.The speed of the wave is 4 n cross times a b
    II.The medium at a will be in the same phase as d after fraction numerator 4 over denominator 3 n end fraction s
    III.The phase difference between b and e is fraction numerator 3 pi over denominator 2 end fraction
    Which of these statements are correct

    The rope shown at an instant is carrying a wave travelling towards right, created by a source vibrating at a frequency n. Consider the following statements

    I.The speed of the wave is 4 n cross times a b
    II.The medium at a will be in the same phase as d after fraction numerator 4 over denominator 3 n end fraction s
    III.The phase difference between b and e is fraction numerator 3 pi over denominator 2 end fraction
    Which of these statements are correct

    physics-General
    General
    physics-

    Intensity level 200 cm from a source of sound is 80 blank d B. If there is no loss of acoustic power in air and intensity of threshold hearing is 10 to the power of negative 12 end exponent W m to the power of negative 2 end exponent then, what is the intensity level at a distance of 4000 cm from source

    Intensity level 200 cm from a source of sound is 80 blank d B. If there is no loss of acoustic power in air and intensity of threshold hearing is 10 to the power of negative 12 end exponent W m to the power of negative 2 end exponent then, what is the intensity level at a distance of 4000 cm from source

    physics-General
    parallel
    General
    physics-

    In a sonometer wire, the tension is maintained by suspending a 50.7 kg mass from the free end of the wire. The suspended mass has a volume of 0.0075 blank m to the power of 3 end exponent. The fundamental frequency of the wire is 260 Hz If the suspended mass is completely submerged in water, the fundamental frequency will become (take g equals 10 blank m s to the power of negative 2 end exponent)

    In a sonometer wire, the tension is maintained by suspending a 50.7 kg mass from the free end of the wire. The suspended mass has a volume of 0.0075 blank m to the power of 3 end exponent. The fundamental frequency of the wire is 260 Hz If the suspended mass is completely submerged in water, the fundamental frequency will become (take g equals 10 blank m s to the power of negative 2 end exponent)

    physics-General
    General
    Maths-

    If ellr means (log log log......), the log being repeated r times, then
    not stretchy integral left curly bracket x l left parenthesis x right parenthesis l to the power of 2 end exponent left parenthesis x right parenthesis l to the power of 3 end exponent left parenthesis x right parenthesis.... l to the power of r end exponent left parenthesis x right parenthesis right curly bracket to the power of negative 1 end exponent d xis equal to

    If ellr means (log log log......), the log being repeated r times, then
    not stretchy integral left curly bracket x l left parenthesis x right parenthesis l to the power of 2 end exponent left parenthesis x right parenthesis l to the power of 3 end exponent left parenthesis x right parenthesis.... l to the power of r end exponent left parenthesis x right parenthesis right curly bracket to the power of negative 1 end exponent d xis equal to

    Maths-General
    General
    physics-

    A man standing between two parallel hills, claps his hand and hears successive echoes at regular intervals of 11s If velocity of sound is 340 m s to the power of negative 1 end exponent comma then the distance between the hills is

    A man standing between two parallel hills, claps his hand and hears successive echoes at regular intervals of 11s If velocity of sound is 340 m s to the power of negative 1 end exponent comma then the distance between the hills is

    physics-General
    parallel
    General
    physics-

    A massless rod is suspended by two identical strings AB and CD of equal length. A block of mass m is suspended from point O such that B Ois equal to ´ ´ x ´ ´ Further, it is observed that the frequency of 1st harmonic (fundamental frequency) in AB is equal to 2nd harmonic frequency in CD. Then, length of BO is

    A massless rod is suspended by two identical strings AB and CD of equal length. A block of mass m is suspended from point O such that B Ois equal to ´ ´ x ´ ´ Further, it is observed that the frequency of 1st harmonic (fundamental frequency) in AB is equal to 2nd harmonic frequency in CD. Then, length of BO is

    physics-General
    General
    physics-

    If the velocity of sound in air is 336 m/s The maximum length of a closed pipe that would produce a just audible sound will be

    If the velocity of sound in air is 336 m/s The maximum length of a closed pipe that would produce a just audible sound will be

    physics-General
    General
    Maths-

    If not stretchy integral fraction numerator sin invisible function application x over denominator sin invisible function application left parenthesis x minus alpha right parenthesis end fraction d x equalsAx + B log sin (x – alpha) + c, then value of (A, B) is –

    If not stretchy integral fraction numerator sin invisible function application x over denominator sin invisible function application left parenthesis x minus alpha right parenthesis end fraction d x equalsAx + B log sin (x – alpha) + c, then value of (A, B) is –

    Maths-General
    parallel
    General
    Maths-

    If integralx sin x dx = – x cos x + alpha, then alpha =

    If integralx sin x dx = – x cos x + alpha, then alpha =

    Maths-General
    General
    maths-

    The equation of the tangent to the parabola y = (x – 3)2 parallel to the chord joining the points (3, 0) and (4, 1) is -

    The equation of the tangent to the parabola y = (x – 3)2 parallel to the chord joining the points (3, 0) and (4, 1) is -

    maths-General
    General
    maths-

    The line x + y = a touches the parabola y = x – x2, and f (x) = sin2 x + sin2 open parentheses x plus fraction numerator pi over denominator 3 end fraction close parentheses+ cosx cos open parentheses x plus fraction numerator pi over denominator 3 end fraction close parentheses, g open parentheses fraction numerator 5 over denominator 4 end fraction close parentheses= 1, b = (gof) (x), then

    The line x + y = a touches the parabola y = x – x2, and f (x) = sin2 x + sin2 open parentheses x plus fraction numerator pi over denominator 3 end fraction close parentheses+ cosx cos open parentheses x plus fraction numerator pi over denominator 3 end fraction close parentheses, g open parentheses fraction numerator 5 over denominator 4 end fraction close parentheses= 1, b = (gof) (x), then

    maths-General
    parallel
    General
    maths-

    If θ be the angle subtended at the focus by the normal chord at the point (λ,λ ),λ ≠ 0 on the parabola y2 = 4ax, then equation of the line through (1, 2) and making and angle θ with x-axis is

    If θ be the angle subtended at the focus by the normal chord at the point (λ,λ ),λ ≠ 0 on the parabola y2 = 4ax, then equation of the line through (1, 2) and making and angle θ with x-axis is

    maths-General
    General
    maths-

    The length of a focal chord of the parabola y2 = 4ax at a distance b from the vertex is c. Then

    The length of a focal chord of the parabola y2 = 4ax at a distance b from the vertex is c. Then

    maths-General
    General
    maths-

    The equation of common tangent to the parabolas y2 = 4ax and x2 = 4by is

    The equation of common tangent to the parabolas y2 = 4ax and x2 = 4by is

    maths-General
    parallel

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.