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The value of int(0)^(pi)(Sigma(r=0)^(3)a...

The value of `int_(0)^(pi)(Sigma_(r=0)^(3)a_(r)cos^(3-r)x sin^(r)x)dx` depends upon

A

`a_(1) and a_(2)`

B

`a_(0)and a_(3)`

C

`a_(2) and a_(3)`

D

`a_(1) and a_(3)`

Text Solution

Verified by Experts

The correct Answer is:
D
Let `l = int_(0)^(pi)sum_(r=0)^(3)a_(r )cor^(3-r)x sin^(r )x dx`
`= int_(0)^(pi) a_(0)cos^(3)x dx + int_(0)^(pi)a_(1)cos^(2)x sin x dx + int_(0)^(pi)a_(2)cos x sin^(2)x dx + int_(0)^(pi)a_(3)sin^(3)x dx`
Since, `int_(0)^(2a)f(x)dx = {{:(2int_(0)^(a)f(x)"dx,",f(2a-x)=f(x)),(" 0",f(2a-x)=-f(x)):}`
`therefore` Integral Ist and IIIrd becomes zero.
Hence, The given integral is depend upon `a_(1)` and `a_(3)`.
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