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If f(x) = int0^pi (t sint dt) / (sqrt(1+...

If `f(x) = int_0^pi (t sint dt) / (sqrt(1+tan^2xsin^2t))` for `0 < x < pi/2`, then (a) `f(0^+)=-pi` (b) `f(pi/4)=(pi^2)/8` (c) `f` is continuous and differentiable in `(0,pi/2)` (d) `f` is continuous but not differentiable in `(0,pi/2)`

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CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. The value of the integral int(e^(-1))^(e^2)|((log)e x)/x| dx is (A)...

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  2. f(x)=int1^xlogt/(1+t+t^2)dt (xge1) then prove that f(x) =f(1/x)

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  3. If f(x) = int0^pi (t sint dt) / (sqrt(1+tan^2xsin^2t)) for 0 < x < pi/...

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  4. Evaluate: int(sqrt(2)-1)^(sqrt(2)+1)((x^2-1))/((x^2+1)^2)dx

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  5. int0^x(2^t)/(2^([t]))dt ,w h e r e[dot] denotes the greatest integer f...

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  6. Ify=int0^xf(t)sin{k(x-t)}dt ,t h e np rov et h a t(d^2y)/(dx^2)+k^2y=k...

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  7. f(x) is a continuous function for all real values of x and satisfies i...

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  8. If x=int0^y (dt)/sqrt(1+9t^2) and (d^2y)/(dx^2)=ay, then find a

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  9. The value of int(1/e)^tanx(tdt)/(1+t^2)+int(1/e)^cotxdt/(t(1+t^2) is

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  10. Prove that: y=int(1/8)^(sin^2x)sin^(-1)sqrt(t)dt+int(1/8)^(cos^2x)cos^...

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

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

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

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

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

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

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

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

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

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