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If `f` is continuous function and `F(x)=int_0^x((2t+3)*int_t^2f(u)d u)dt ,` then `|(F''(2))/(f(2))|` is equal to_____

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CENGAGE ENGLISH-INTEGRALS-All Questions
  1. For any real number x, let [x] denote the largest integer less than or...

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

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

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  4. Let f^(prime)(x)=(192 x^3)/(2+sin^4pix)fora l lx in Rw i t hf(1/2)=0....

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

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  6. f(x)=int0^x f(t) dt=x+intx^1 tf(t)dt, then the value of f(1) is

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

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

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

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

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

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

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

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

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  15. Let f(x)=int2^x (dt)/sqrt(1+t^4) and g be the inverse of f. Then, the...

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

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

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  18. If f(x)=cosx-int0^x(x-t)f(t)dt ,t h e nf^(primeprime)(x)+f(x) is equa...

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

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

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