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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 ENGLISH-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 the following: int(-pi)^(pi)(1-x^(2))sinx cos^(2)x dx

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

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  8. Evaluate the following: int(-1//2)^(1//2)cos x "log" (1-x)/(1+x)dx

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  9. int(-(3pi)/2)^(-pi/2) {(pi+x)^3+cos^2(x+3pi)}dx is equal to (A) pi/4-1...

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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 , then find the value of k

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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,t h e ne v a l u a t e(...

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

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  19. Evaluate (lim)(xvec4)int4^x((4t-f(t)))/((x-4))dt

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  20. Evaluate: ("lim")(xvec2)(int0"x"cost^2dt)/x

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