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If I1=int0^pixf(sin^3x+cos^2x)dxand I2=...

If `I_1=int_0^pixf(sin^3x+cos^2x)dxand` `I_2=int_0^(pi/2)f(sin^3x+cos^2x)dx , then relate I_1 and I_2`

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The correct Answer is:
`I_(1)=piI_(2)`
`I_(1)=int_(0)^(1)(pi-x)f(sin^(3)x+cos^(2)x)dx`
`:. 2I=pi int_(0)^(pi)f(sin^(3)x+cos^(2)x) dx`
`=2pi int_(0)^(pi//2) f(sin^(3)x+cos^(2)x)dx`
or `I_(1)=pi int_(0)^(pi//2) f(sin^(3)x+cos^(2)x)dx=piI_(2)`
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CENGAGE PUBLICATION-DEFINITE INTEGRATION -CAE_TYPE
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  2. Evaluate int(-oo)^(0)(te^(t))/(sqrt(1-e^(2t)))dt

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  3. If I1=int0^pixf(sin^3x+cos^2x)dxand I2=int0^(pi/2)f(sin^3x+cos^2x)dx ...

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  4. Evaluate: int(-pi/2)^(pi/2)sin^2xcos^2x(sinx+cosx)dx

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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