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Evaluate: int1^a xdota^(-[(log)a x])dx ,...

Evaluate: `int_1^a xdota^(-[(log)_a x])dx ,(a >1)dot`

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CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. Prove that: y=int(1/8)^(sin^2x)sin^(-1)sqrt(t)dt+int(1/8)^(cos^2x)cos^...

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  2. f(x)>0AAx in R and is bounded. If lim(n->oo)[int0^a(f(x)dx)/(f(x)+f(a...

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  3. Evaluate: int1^a xdota^(-[(log)a x])dx ,(a >1)dot

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  4. int0^oo(sin^2x)/(x^2)dx must be same as:

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  5. Evaluate: int1^(e^6)[(logx)/3]dx ,w h e r e[dot] denotes the greatest...

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  6. If int(0)^(oo) (sinx)/x dx=(pi)/2, then int(0)^(oo) (sin^(3)x)/x dx i...

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  7. Find the value of int(-1)^(1)[x^(2)+{x}]dx, where [.] and {.} denote t...

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  8. int0^x[cost]dt ,w h e r ex in (2npi,2npi+pi/2),n in N ,and [dot] den...

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  9. Prove that int0^x[cot^(-1)x]dx ,w h e r e[dot] denotes the greatest in...

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  10. Evaluate: int(-pi/2)^(2pi)[cot^(-1)x]dx , where [dot] denotes the grea...

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  11. f(x) is continuous function for all real values of x and satisfies int...

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  12. Prove that int0^1xe^xdx=1

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  13. I1=int0^(pi/2)ln(sinx)dx ,I2=int(-pi/4)^(pi/4)ln(sinx+cosx)dxdot Then ...

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  14. Prove that int0^oo[n e^(-x)]dx=ln((n^n)/(n !)),w h e r en is a na...

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  15. For x in R and a continuous function f, let I1=int(sin^2t)^(1+cos^2t)...

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  16. Evaluate of each of the following integrals int(pi//6)^(pi//3)(sqrt...

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  17. Given a function f:[0,4]toR is differentiable ,then prove that for som...

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  18. Evaluate: int0^(pi/2)log((4+3sinx)/(4+3cosx))dx

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  19. The value of int0^1 4x^3 {d^2/(dx^2) (1 - x^2)^5 } dx is

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  20. Evaluate: int(-pi)^(3pi)log(s e c theta-t a ntheta)d theta

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