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If f(x)=(sinx)/xAAx in (0,pi], prove tha...

If `f(x)=(sinx)/xAAx in (0,pi],` prove that `pi/2int_0^(pi/2)f(x)f(pi/2-x)dx=int_0^pif(x)dx`

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CENGAGE PUBLICATION-INTEGRALS-All Questions
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  3. If f(x)=(sinx)/xAAx in (0,pi], prove that pi/2int0^(pi/2)f(x)f(pi/2-x)...

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  6. If f(x+f(y))=f(x)+yAAx ,y in R and f(0)=1, then prove that int0^2f(2-...

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  7. Let intx^(x+p)f(t)dt be independent of xa n dI1=int0^pf(t)dt ,I2=int(1...

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  8. Evaluate: int3^10[log[x]]dx

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  9. If the function f : [0,8] to R is differentiable, then for 0 < alpha...

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  12. Evaluate:int-pi^pi ((2x)(1+sinx)/(1+cos^2x))dx

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  14. Let f(x) be a derivable function satisfying f(x)=int0^x e^tsin(x-t)dt...

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  15. If int0^1 e^(x^2)(x-alpha)dx=0, then (a)alphalt2 (b)alphalt0 (c)"" 0l...

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  16. int(5/2)^5(sqrt((25-x^2)^3))/(x^4)dx is equal to

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  18. Let f(0)=0a n dint0^2f^(prime)(2t)e^(f(2t))dt=5.t h e nv a l u eoff(4)...

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  19. The value of the integral int0^oo(xlogx)/((1+x^2)^2)dx ,is (a)0 (...

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