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If F(x) = int(x^(2))^(x^(3)) log t dt ,(...

If `F(x) = int_(x^(2))^(x^(3)) log t dt ,( t gt 0)` then `F^(')(x)` is equal to

A

`(9x^(2)-4x)log x`

B

`(4x-9x^(2))log x`

C

`(9x^(2)+4x)log x`

D

none of these

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The correct Answer is:
A
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HIMALAYA PUBLICATION-Definite Integrals and its Application-QUESTION BANK
  1. int(-1)^(0) (9x^(2)+2x+2 ) dx=

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  2. int(-1)^(1) log (x+sqrt(x^(2)+1))dx =

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  3. If F(x) = int(x^(2))^(x^(3)) log t dt ,( t gt 0) then F^(')(x) is equa...

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  4. int0^(pi) e^(sin^(2)x). cos^(3) x dx =

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  5. The value of int0^(1) (dx)/(x+sqrt(1-x^(2))) dx

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  6. inta^(b) (sqrtx dx)/(sqrtx + sqrt(a+b-x)) =

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  7. The value of int2^(3) (x+1)/(x^(2)(x-1)) dx =

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  8. If g(x) = (f(x)-f(-x))/2 defined over [-3,3] and f(x) = 2x^(2)-4x+1, t...

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  9. int0^(pi/4) (cos x- sin x) dx + int(pi/4)^((5pi)/4) (sinx-cosx) dx + i...

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  10. The value of the integral int0^(oo) log(x+1/x) (dx)/(x^2 +1) is

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  11. If f: R rarr R and g:R rarr R are one-to-one, real valued functions, t...

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  12. If int(log2)^(x) (du)/((e^(u)-1)^(1/2)) = pi/6, then e^(x) =

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  13. The value of int0^(sin^(2)theta) sin^(-1) sqrtphi dphi + int0^(cos^(2)...

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  14. int0^(10pi) |sin x| dx is

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  15. int(-pi)^(pi) (2x(1 + sin x))/(1 + cos^2 x) dx is :

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  16. int0^(sqrt2) [x^(2)] dx = , wher [x] is the greatest integer function

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  17. If P = int0^(3pi) f(cos^(2)x) dx and Q = int0^(pi) f(cos^(2)x) dx then

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  18. If int0^(1) (x^(7))/(sqrt(1-x^(4))) dx =

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  19. Let I(1) = inta^(pi-a) xf (sin x) dx, I(2) = inta^(pi-a) f(sinx) dx th...

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  20. The value of the integral int(1/n)^(((an-1))/(n)) sqrtx/(sqrt(a-x) + s...

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