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If f(x) = int(2x)^(sinx) cos (t^(3)) dt ...

If `f(x) = int_(2x)^(sinx) cos (t^(3)) dt` then `f '(x)`

A

`cos(sin^(3)x).cosx- 2cos(8x^(3))`

B

`sin(sin^(3)x).sin x- 2sin(8x^(3))`

C

`cos(cos^(3)x).cos x- 2cos(x^(3))`

D

`sin(sin^(3)x).cos x- 2sin(8x^(3))`

Text Solution

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The correct Answer is:
A
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HIMALAYA PUBLICATION-Definite Integrals and its Application-QUESTION BANK
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  2. If f(x) be a continous function for all real values of x and satisfies...

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  3. If f(x) = int(2x)^(sinx) cos (t^(3)) dt then f '(x)

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  4. Iff(x) = int1^(x^(2)) tan^(-1) sqrtt dt, t gt 0, then f^(')(1)=

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

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  6. If f(x) is differentiable and int0^(t^2) x f(x) dx = 2/5 t^5, then f (...

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  7. Equation of the tangent to y= int(x^(2))^(x^(3)) (dt)/(sqrt(1+t^(2)))...

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  8. If inta^(x) f(t) dt - int0^(y) g(t) dt = b then dy/dx at (x(0),y(0)) i...

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  9. If f(x) = 1/x^(2) int2^(x)[t^(2)+f^(')(t)]dt, then f^(')(2) =

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  10. If inta^(x) [f(t) - 3t] dt = a^(2)-x^(2) then f(pi/6) =

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

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  12. If f and g are continuous [0,a) satisfying f(x) = f(a-x) and g(x)+ g(a...

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  13. Let f : [1, oo) rarr [2, oo) be a differentiable function such that f(...

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  14. The critical point of : f(x) = 1 + x + int1^x [(log t)^2 + 2 log t] ...

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  15. If f(pi) = 2 and int0^(pi) [f(x)+f^('')(x)] sin x dx = 5 then f(0)

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  16. int(-1)^(1) d/(dx) (1/(1+e^(1/x))) dx =

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  17. inta^(b) f(x) dx is equal to

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  18. If f and g are continuous functions in [0,1] satisfying f(x) = f(a - x...

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  19. If x=int0^(y) (dt)/(sqrt(1+9t^(2))) and (d^(2)y)/(dx^(2)) = ay, then a...

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  20. int(-1)^(1) (x^3 + |x| + 1)/(x^2 + 2|x| + 1) dx is equal to :

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