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The value of int(0)^(2pi)[sin2x(1+cos3x)...

The value of `int_(0)^(2pi)[sin2x(1+cos3x)]` dx, where [t] denotes

A

`-pi`

B

`2pi`

C

`pi`

D

`-2pi`

Text Solution

Verified by Experts

The correct Answer is:
A
`int_(0)^(2pi)[sin2x(1+cos 3x)]dx`
Let `I=int_(0)^(2pi)[sin2x(1+cos3x)]dx`…………..(1)
`I=int_(0)^(2pi)[sin2(2pi-x)(1+cos3(2pi-x)]dx`
`I=int_(0)^(2pi)[-sin2x(1+cos 3x)]dx`……………(ii)
(1) + (2)
`2I = int_(0)^(2pi)(-1)dx`
`[x] +[-x]=-1`
`2z =-2pi rArr I=-pi`
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