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Maths-

General

Easy

Question

The value of $not stretchy integral subscript 0 end subscript superscript pi end superscript open vertical bar sin to the power of 3 end exponent invisible function application rightwards arrow over short leftwards arrow theta close vertical bar d theta$ is

0
3/8
4/3
$π$

The correct answer is: 4/3

$I equals not stretchy integral subscript 0 end subscript superscript pi end superscript vertical line sin to the power of 3 end exponent invisible function application theta vertical line d theta$
Since $sin invisible function application theta$ is positive in interval $left parenthesis 0 comma pi right parenthesis$
$therefore I equals not stretchy integral subscript 0 end subscript superscript pi end superscript sin to the power of 3 end exponent invisible function application theta d theta equals not stretchy integral subscript 0 end subscript superscript pi end superscript sin invisible function application theta left parenthesis 1 minus cos to the power of 2 end exponent invisible function application theta right parenthesis d theta$
$equals not stretchy integral subscript 0 end subscript superscript pi end superscript sin invisible function application theta d theta plus not stretchy integral subscript 0 end subscript superscript pi end superscript left parenthesis negative sin invisible function application theta right parenthesis cos to the power of 2 end exponent invisible function application theta d theta$
$equals left square bracket negative cos invisible function application theta right square bracket subscript 0 end subscript superscript pi end superscript plus open parentheses fraction numerator cos to the power of 3 end exponent invisible function application theta over denominator 3 end fraction close parentheses subscript 0 end subscript superscript pi end superscript equals fraction numerator 4 over denominator 3 end fraction$ .

Related Questions to study

A spherical shell, made of material of electrical conductivity $fraction numerator 10 to the power of 9 end exponent over denominator pi end fraction left parenthesis capital omega minus m right parenthesis to the power of negative 1 end exponent$ has + - thickness t = 2 mm and radius r = 10 cm. In an arrangement, its inside surface is kept at a lower potential than its outside surface The resistance offered by the shell is equal to
"

A spherical shell, made of material of electrical conductivity $fraction numerator 10 to the power of 9 end exponent over denominator pi end fraction left parenthesis capital omega minus m right parenthesis to the power of negative 1 end exponent$ has + - thickness t = 2 mm and radius r = 10 cm. In an arrangement, its inside surface is kept at a lower potential than its outside surface The resistance offered by the shell is equal to
"

physics-General

In the shown wire frame, each side of a square (the smallest square) has a resistance R. The equivalent resistance of the circuit between the points A and B is :

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A cell of emf E having an internal resistance 'r ' is connected to an external resistance R. The potential difference ' V ' across the resistance R varies with R as shown by the curve:

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physics-General

In a practical wheat stone bridge circuit as shown, when one more resistance of 100 W is connected is parallel with unknown resistance ' x ', then ratio $l subscript 1 end subscript$ ₁ $l subscript 2 end subscript$ become ' 2 '. l1 is balance length. AB is a uniform wire. Then value of ' x ' must be:

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In the shown arrangement of the experiment of the meter bridge if AC corresponding to null deflection of galvanometer is x, what would be its value if the radius of the wire AB is doubled?

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physics-General

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physics-General

In which of the following case current shown by ammeter is maximum

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parallel

In $triangle A B C comma angle B colon angle C equals 3 colon 2 comma angle B$ then find $angle B$ in the figure.

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A wire has resistance of 24 W is bent in the following shape. The effective resistance between A and B is

A wire has resistance of 24 W is bent in the following shape. The effective resistance between A and B is

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if $y equals 2 x comma z equals 3 x comma r equals 4 x$ then find y in the given figure.

parallel

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