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IfIn=int0^pie^x(sin"x")^("n")dx ,t h e n...

`IfI_n=int_0^pie^x(sin"x")^("n")dx ,t h e n(I_3)/(I_1)"is equal to"` (a) `3/5` (b) `1/5` (c) 1 (d) `2/5`

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CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. Let g(x)=int0^x f(t).dt,where f is such that 1/2<=f(t)<=1 for t in [0,...

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  2. The value of int0^(pi/2) sin|2x-alpha|dx, where alpha in [0,pi], is (...

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  3. IfIn=int0^pie^x(sin"x")^("n")dx ,t h e n(I3)/(I1)"is equal to" (a) 3/...

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  4. int(-2)^0{(x+1)^3+2+(x+1)cos(x+1)dx is equal to (A) -4 (B) 0 (C) 4 ...

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  5. For any real number x, let [x] denote the largest integer less than or...

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  6. evaluate: int0^(pi/4)2tan^3xdx is

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  7. If f is continuous function and F(x)=int0^x((2t+3)*intt^2f(u)d u)dt , ...

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  8. Let f'(x)=(192x^3)/(2+sin^4pix) for all x in R with f(1/2)=0.If mleint...

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  9. If the value of lim(n rarr oo)(n^(-3/2)) sum(j=1)^(6n) sqrt(j) is equa...

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  10. If int0^xf(t) dt=x+intx^1 tf(t)dt, then the value of f(1)

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

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  12. The value of int1^a[x]f^(prime)(x)dx ,where a >1, and [x] denotes the ...

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  13. The value of int(0)^(x)[cost]dt, x epsilon[(4n+1)(pi)/2,(4n+3)(pi)/2] ...

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  14. Let f(x)=min({x},{-x})AA epsilonR, where {.} denotes the fractional pa...

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  15. int1^4 {x-0.4}dx equals (where {x} is a fractional part of x

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

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

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

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

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