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int0^(2pi)sin^(100)xcos^(99)x dx equals ...

`int_0^(2pi)sin^(100)xcos^(99)x dx` equals to ?

Text Solution

Verified by Experts

The correct Answer is:
`0`
`I=int_(0)^(2pi)sin^(100)xcos^(99)x dx`
Here `f(x)=sin^(100)x cos^(99) x` for which `f(2pi-x)=f(x)`
`:.I=2int_(0)^(pi)sin^(100)xcos^(99)xdx`
`=2int_(0)^(pi)sin^(100)(pi-x)cos^(99)(pi-x)dx`
`=-2int_(0)^(pi)sin^(100)xcos^(99)xdx`
`=-I`
or `2I=` or `I=0`
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CENGAGE PUBLICATION-DEFINITE INTEGRATION -CAE_TYPE
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  3. int0^(2pi)sin^(100)xcos^(99)x dx equals to ?

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  11. Evaluate: int(-pi)^pi(1-x^2)sinxcos^2xdx

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  12. Evaluate: int(-1)^1(sinx-x^2)/(3-|x|)dx

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  14. Evaluate: int(-(3pi)/2)^(-pi/2)[(x+pi)^3+cos^2(x+3pi)]dx

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  15. Evaluate: int0^(100)(x-[x]dx(w h e r e[dot] represents the greatest i...

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  16. Evaluate: int0^(100pi)sqrt((1-cos2x))dxdot

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  17. Ifint0^(npi)f(cos^2x)dx=kint0^pif(cos^2x)dx ,t h e nfin dt h ev a l u ...

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  18. Evaluate int(0)^(npi+t)(|cosx|+|sinx|)dx, where n epsilonN and t epsil...

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