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If f(x)=inta^x[f(x)]^(-1)dx and inta^1[f...

If `f(x)=int_a^x[f(x)]^(-1)dx` and `int_a^1[f(x)]^(-1)dx=sqrt(2)`, then

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CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. If f^(prime)(x)=f(x)+int0^1f(x)dx ,gi v e nf(0)=1, then the value of ...

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  2. STATEMENT 1: int0^pisqrt(1-sin^2x) dx=0 , STATEMENT 2: int0^picosx dx...

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  3. STATEMENT 1: Let m be any integer. Then the value of Im=int0^pi(sin2m ...

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  4. STATEMENT 1: inta^xf(t)dt is an even function if f(x) is an odd functi...

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  5. STATEMENT 1: The value of int0^(2pi)cos^(99)x dx is 0 STATEMENT 2: in...

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  6. For a epsilonR (the set of all real numbers) a!=-1, lim(n to oo) ((1^(...

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  7. Let S be the area of the region enclosed by y=e^(-x^(2)),y=0, x=0 and ...

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  8. Let f : (0,infty) rarr R be given by f(x) = int(1/x)^(x) e^-(t + 1/t...

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  9. Show that int0^pixf(sinx)dx=pi/2int0^pif(sinx)dxdot

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  10. Let f(x) be a non-constant twice differentiable function defined on (-...

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  11. Let f(x)=int2^x(dt)/(sqrt(1+t^4))a n dg(x) be the inverse of f(x) . Th...

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  12. Let f be a real-valued function defined on interval (0,oo),by f(x)=lnx...

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  13. Let f: R rarr R be a continuous odd function, which vanishes exactly a...

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  14. If the value of the definite integral int0^1(sin^(-1)sqrt(x))/(x^2-x+1...

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  15. Let f(x)=7tan^8x+7tan^6x-3tan^4x-3tan^2x for all x in (-pi/2, pi/2). T...

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  16. The option(s) with the values of a and L that satisfy the following eq...

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  17. Let f: R->R be a function defined by f(x)={[x],(xlt=2) \ \ (0,x >2) ...

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  18. Prove that int0^1tan^(-1)(1/(1-x+x^2))dx=2int0^1tan^(-1)x dx. Hence ...

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  19. Let f(x)=|[secx,cosx,sec^2x+cotxcos ecx],[cos^2x,cos^2x, cosec^2x],[1,...

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  20. If f(x)=inta^x[f(x)]^(-1)dx and inta^1[f(x)]^(-1)dx=sqrt(2), then

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