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The value of int(0)^(x)[cost]dt, x epsil...

The value of `int_(0)^(x)[cost]dt, x epsilon[(4n+1)(pi)/2,(4n+3)(pi)/2]` and `n epsilonN` is equal to (where [.] represents greatest integer function.

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CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. If I=int0^((3pi)/4)[(1+x)sinx+(1-x)cosx]dx , then value of (sqrt(2)-1...

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  6. The value of the definite integral int2^4(x(3-x)(4+x)(6-x)(10-x)+sinx...

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  7. Ifx=intc^(sint)sin^(-1)z dz ,y=intk^(sqrt(t))(sinz^2)/zdz ,t h e n(dy)...

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  8. If f(x)=int0^1(dt)/(1+|x-t|) ,then f^(prime)(1/2) is equal to (a)0 ...

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  9. 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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  10. STATEMENT 1: int0^(pi/4)log(1+t a ntheta)d theta=pi/8log2. STATEMENT...

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  11. STATEMENT 1:f(x) is symmetrical about x=2 . Then int(2-a)^(2+a)f(x)dx ...

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  13. If f^(prime)(x)=f(x)+int0^1f(x)dx ,gi v e nf(0)=1, then the value of ...

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

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

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

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

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

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

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

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