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int(0)^(100pi)(sum(r=1)^(10)tanrx)dx is ...

`int_(0)^(100pi)(sum_(r=1)^(10)tanrx)dx` is equal to

A

0

B

`100pi`

C

`-50pi`

D

`50pi`

Text Solution

Verified by Experts

The correct Answer is:
A
`I=int_(0)^(100pi)(tanx+tan2x+tan3x+...+tan10x)dx`
Period of `f(x)=tanx+tan2x+...+tan10x" is "pi`
`therefore" "I=100int_(0)^(pi)(tanx+tan2x+tan3x+...+tan10x)dx`
Now, `f(x)=-f(pi-x)`
`therefore" "I=0`
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