If f (x) = \sin^5 x + \sin^3 x and g (x) = \cos^5 x + \sin^3 x , then the value of \int^{\pi/2}_{0} [f (x) + f (-x)] [g(x) + g (-x)] dx is

NIMCET 2018 Question Paper with solutions

Question : 18 of 120

Marks: +1, -0

If f (x) =

sin^5 x + sin^3 x

and g (x) =

cos^5 x + sin^3 x

, then the value of

∫↖{π/2}↙{0}

[f (x) + f (-x)] [g(x) + g (-x)] dx is

Solution:

f (-x) =

sin^5(-x)+sin^3(-x)

-sin^5x-sin^3x

= -

(sin^5x+sin^3x)

⇒ f (-x) = - f (x)
⇒ f (-x) + f (x) = f (x) - f (x) = 0
∴

∫↖{π\/2}↙{0}

[f () + f (-x)] [g (x) + g (-x)] dx
=

∫↖{π\/2}↙{0}

0 . [g (x) + g (-x) dx] = 0

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