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Evaluate: ifintf(x)dx=g(x),t h e nintf^(...

Evaluate: `ifintf(x)dx=g(x),t h e nintf^(-1)(x)dx`

A

`xf ^(-1) (x) +C`

B

`f (g ^(-1) (x)) +C`

C

`xf ^(-1) (x)-g(f ^(-1) (x)) +C`

D

`g ^(-1) (x) +C`

Text Solution

Verified by Experts

The correct Answer is:
C
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DISHA PUBLICATION-INTEGRALS -EXERCISE-2 CONCEPT APPLICATOR
  1. If |x| lt 1" thn "underset(n to oo)"Lt "(1+x)(1+x^(2))(1+x^(4))....(1+...

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  2. int0^1000 e^(x-[x])dx

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  3. Evaluate: ifintf(x)dx=g(x),t h e nintf^(-1)(x)dx

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  4. int(-pi/4) ^(pi/4) (e^theta(thetasintheta))/(e^(2theta)-1)d theta=

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  5. int (x ^(n-1))/( x ^(2n) + a ^(2)) dx =

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  6. If intf(x)cos x dx = 1/2 f^(2)(x)+C, then f(x) can be

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  7. Evaluate: int2^2^x2^2^xdxdot

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  8. The value of int (sqrt ( log 2 )) ^(sqrt( log 3 )) (x sin x ^(2))/( si...

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  9. The value of int((1+x))/(x(1+x e^(x))^(2))dx, is equal to

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  10. The value of int((ax^2-b)dx)/(xsqrt(c^2x^2-(ax^2+b)^2)) is equal to

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  11. int(log sqrt(pi//2))^(log sqrt(pi))e^(2x)sec^(2)((1)/(3)e^(2x))dx=

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  12. Evaluate : int(6x+7)/(sqrt((x-5)(x-4)))\ dx

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  13. Evaluate: intx/((x-1)(x^2+4))dx

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  14. int sqrt(5+x^2)/x^4\ dx=

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  15. If f(x) = pe^(2x) + qe^x + rx satisfies the condition f(0)=-1, f' (I...

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  16. The value of int 0^(sin^2x)sin^(-1)sqrt(t)dt+int 0^(cos^2x)cos^(-1)sqr...

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  17. Find int ( 0) ^(pi//2) cos ^(3) x

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  18. What is int(0)^(pi//2) (dx)/(a^(2) cos^(2) x+ b^(2) sin^(2) x) equal t...

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  19. Let f : R to R be a differentiable function and f(1) = 4. Then, the va...

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  20. Let F (x) = f(x) + f ((1)/(x)), where f (x) = int (1) ^(x ) (log t)/(1...

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