1
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Question

# If ∫(√1+sin x)f(x)dx=23 (1+sin x)3/2+C,then f(x) is .

A
cos x
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B
sin x
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C
tan x
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D
1
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Solution

## The correct option is A cos xHere, the important thing to remember is that integration is the reverse process of differentiation i.e. If ∫g(x)dx=F(x)+C , then dF(x)dx=g(x). Here, let∫g(x)dx=∫(√1+sinx)f(x) dx⇒g(x)=(√1+sinx)f(x)also F(x)=23 (1+sinx)3/2+C⇒∫g(x)=F(x)⇒g(x)=dF(x)dx Thus, substituting the function values in the above equation we get,ddx(23 (1+sinx)3/2+C)=f(x)√1+sinx ⇒23.32 (1+sinx)1/2cos x=f(x)√1+sinx ⇒(1+sinx)1/2cos x=f(x)√1+sinx ⇒cos x=f(x)

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