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Question

If x enotes the rounded off value of x $left parenthesis 3.4 equals 3 comma 3.5 equals 4 comma 3.8 equals text 4etc end text right parenthesis$ and the area bounded by the two curves defined by y = $vertical line x minus x with not stretchy bar on top vertical line$ and $y equals lambda sin invisible function application left parenthesis pi x right parenthesis comma lambda 1$ . In the interval 0 x 1 is equal to 2 square units, The value of the constant is

$\frac{7 π}{8}$
$\frac{5 π}{8}$
$\frac{9 π}{8}$
none of these

The correct answer is: $fraction numerator 9 pi over denominator 8 end fraction$

0 < 0.5 = 0 y = |x 0| = x
0.5 x 1, = 1 y = |x 1| = 1 x

given that $stretchy integral subscript 0 end subscript superscript 1 end superscript lambda s i n invisible function application left parenthesis pi x right parenthesis minus fraction numerator 1 over denominator 2 end fraction$ x(1) (0.5)
= 2 = 2 + =
$open fraction numerator lambda c o s invisible function application left parenthesis pi x right parenthesis over denominator pi end fraction close vertical bar subscript b end subscript superscript 1 end superscript$ 


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