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

Evaluate: `int_(-pi)^pi(1-x^2)sinxcos^2xdx`

Text Solution

Verified by Experts

The correct Answer is:
`0`
Value `=0` since `(1-x^(2)) sinx cos^(2)x` is an odd function of `x`.
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CENGAGE PUBLICATION-DEFINITE INTEGRATION -CAE_TYPE
  1. Evaluate: int(-pi/2)^(pi/2)sin^2xcos^2x(sinx+cosx)dx

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

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

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

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  5. Evaluate: int(-1/2)^(1/2)cosxlog(1-x)/(1+x)dx

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

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

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

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

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  11. Find the value of : int0^(10)e^(2x-[2x])d(x-[x])w h e r e[dot] denote...

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  12. If f(x) is a function satisfying f(x+a)+f(x)=0 for all x in R and pos...

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  13. Show that int0^(npi+v)|sinx|dx=2n+1-cosv , where n is a positive integ...

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  14. Ifint(pi/3)^xsqrt((3-sin^2t))dt+int0^ycostdt=0,then evaluate (dy)/(d...

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  15. Iff(x)=e^(g(x))a n dg(x)=int2^x(tdt)/(1+t^4), then find the value of ...

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  16. Evaluate (lim)(x to 4)int4^x((4t-f(t)))/((x-4))dt

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  17. Evaluate: lim(xto0)(int(0)^(x^(2))cos^(2)tdt)/(xsinx)

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  18. Find the points of minima for f(x)=int0^x t(t-1)(t-2)dt

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  19. Find the equation of tangent to y=int(x^2)^(x^3)(dt)/(sqrt(1+t^2))a t...

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  20. I f f(x)=int((pi^2)/(16))^(x^2)(sinxsinsqrt(theta))/(1+cos^2sqrt(theta...

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