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If int0^ycost^2dt=int0^(x^2)(sint)/t dt ...

If `int_0^ycost^2dt=int_0^(x^2)(sint)/t dt ,t h ep rov et h a t(dy)/(dx)=(2sinx^2)/(xcosy^2)`

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CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. A function f is continuous for all x (and not everywhere zero) such th...

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  2. If int(cosx)^1(t^2f(t)dt=1-cosx AA x in (0,pi/2), then the value of [...

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  3. If int0^ycost^2dt=int0^(x^2)(sint)/t dt ,t h ep rov et h a t(dy)/(dx)=...

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  6. If f(x)=1+1/x int1^x f(t) dt, then the value of f(e^-1) is

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  7. If int0^1e^ (-x^2) dx=a , then find the value of int0^1x^2e^ (-x^2) dx...

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  8. Ifint0^(f(x))t^2dt=xcospix ,t h e nf^(prime)(9)i s -1/9 (b) -1/3 (c...

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  9. IfIn=int0^pix^nsinx dx ,t h e n fin d t h e v a l u eof I5+20 I3dot

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  11. If I(n)=int(0)^(pi/2) sin^(n)x dx, then show that I(n)=((n-1)/n)I(n-2)...

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  13. If In=int0^1(dx)/((1+x^2)^n); n in N , then prove that 2nI(n+1)=2^(-n...

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  14. Given that f satisfies |f(u)-f(v)|lt=|u-v| for u and v in [a , b]dot T...

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  15. IfIn=int0^1x^n(tan^(-1)x)dx ,t h e np rov et h a t (n+1)In+(n-1)I(n-2...

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  16. IfI=int(-20pi)^(20pi)|sinx|[sinx]dx(w h e r e[dot] denotes the greate...

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  17. IfIm=int1^x(logx)^mdx satisfies the relation (Im)=k-l I(m-1) then A)k...

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  18. The value of the integral int0^1sqrt((1-x)/(1+x))dx i s (a)pi/2+1 (b...

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