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Given that, F(x)=(1)/(x^(2))int(4)^(x)(4...

Given that, `F(x)=(1)/(x^(2))int_(4)^(x)(4t^(2)-2F'(t))dt`, find `F'(4)`.

A

32

B

`32//3`

C

`32//9`

D

none of these

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Verified by Experts

The correct Answer is:
C
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OBJECTIVE RD SHARMA ENGLISH-DEFINITE INTEGRALS-Exercise
  1. The value of integral int(-2)^(4) x[x]dx is

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  2. If h(a)=h(b), the value of the integral inta^b [f(g(h(x))]^(-1)f'(g...

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  3. Given that, F(x)=(1)/(x^(2))int(4)^(x)(4t^(2)-2F'(t))dt, find F'(4).

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  4. It is known that f(x) is an odd function in the interval [p/2, p/2] an...

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  5. Suppose for every integer n, . underset(n)overset(n+1)intf(x)dx = n^(2...

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  6. int(-pi+4)^(pi//4) (tan^(2)x)/(1+a^(x))dx is equal to

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  7. The value of int(0)^(pi//2) cosec(x-pi//3)cosec(x-pi//6)dx is

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  8. The value of int(-1)^(1)(x|x|)dx is equal to

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  9. int0^3 |x^(3)+x^(2)+3x|dx is equal to

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  10. Evaluate: int(-1)^1(x^3+|x|+1)/(x^2+2|x|+1)dx

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  11. Evaluate: int(-pi/2)^(pi/2)log{(a x^2+b x+c)/(a x^2-b x+c)(a+b)|sinx|}...

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  12. For any natural number n, the value of the integral int(0)^(sqrt(n))...

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  13. For any n in R^(+), the value of the integral int(0)^(n[x]) (x-[x])d...

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  14. Let d/(dx)F(x)=((e^(sinx))/x),x > 0. If int1^4 3/x e^sin (x^3)dx=F(...

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  15. The equation int(-pi//4)^(pi//4) {a|sin x|+(b sin x)/(1+cos x)+c}dx=...

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  16. Let f(x) be a continuous function such that f(a-x)+f(x)=0 for all x in...

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  17. The value of int(alpha)^(beta) x|x|dx, where a lt 0 lt beta, is

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  18. int(-pi//2)^(pi//2) (|x|)/(8 cos^(2)2x+1)dxhas the value

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  19. If [.] denotes the greatest integer function and f(x)={:{(3(x)-(5|x|...

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  20. Find the value of int(-1)^(1)[x^(2)+{x}]dx, where [.] and {.} denote t...

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