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If int(sqrt(1-x^2))/x^4dx=A(x) (sqrt(1-x...

If `int(sqrt(1-x^2))/x^4dx=A(x) (sqrt(1-x^2))^m+C`,for a suitable chosen integer m and a function A(x), where C is a constant of integration, then `(A(x))^m` equals

A

`(-1)/(3x^(2))`

B

`-(1)/(27x^(9))`

C

`(1)/(9x^(4))`

D

`(1)/(27x^(6))`

Text Solution

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The correct Answer is:
B
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MCGROW HILL PUBLICATION-INDEFINITE INTEGRATION-QUESTION FROM PREVIOUS YEARS.AIEEE/JEE MAIN PAPERS
  1. The integral int(dx)/(x^(2)(x^(4)+1)^(3//4)) equal

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  2. The integral I = int (dx)/((x+1)^(3//4)(x-2)^(5//4)) is equal to

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  3. if I=int(log(t+sqrt(1+t^2)))/sqrt(1+t^2)dt=1/2(g(t))^2+c then g(2) is ...

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  4. The integral int(2x^(12)+5x^(9))/((x^(5)+x^(3)+1)^(3))dx is equal to ...

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  5. The integral int(1)/((1+sqrt(x))sqrt(x-x^(2)))dx is equal to (where C ...

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  6. If int(1)/(cos^(2)xsqrt(2 sin2x))dx=(tanx)^(A)+C(tanx)^(B)+k, where k...

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  7. Evaluate: intsqrt(1+2cotx(cotx+cosecx))dx

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  8. I ff((3x-4)/(3x+4))=x+2, x!=4/3,andintf(x)dx=Alog|1-x|+B x+C then orde...

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  9. Let In=int tan^n x dx, (n>1). If I4+I6=a tan^5 x + bx^5 + C, Where C...

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  10. If int (2x + 5 )/(sqrt(7 - 6 x - x ^ 2 )) dx = A sqrt (7 - ...

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  11. if f ((x- 4 ) /(x + 2 )) = 2 x + 1 , (x in R - { 1, - 2 }) , ...

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  12. int\ (sin^2 x cos^2x)/(sin^5x+cos^3xsin^2x+sin^3xcos^2x+cos^5x)^2 \ d...

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  13. If int (x+1)/(sqrt(2x-1))dx = f(x)sqrt(2x-1)+C, where C is a constant ...

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  14. int(3x^(13)+2x^(11))/((2x^4+3x^2+1)^4)dx

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  15. If int(sqrt(1-x^2))/x^4dx=A(x) (sqrt(1-x^2))^m+C,for a suitable chose...

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  16. If int x^(5)e^(-x^(2))dx = g(x)e^(-x^(2))+C, where C is a constant of ...

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  17. Let n ge 2 be a natural number and 0 lt theta lt (pi)/(2), Then, int (...

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  18. If f(x) = int(5x^(8)+7x^(6))/((x^(2)+1+2x^(7))^(2))dx, (x ge 0), and f...

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  19. For x ^ 2 ne n pi + 1, n in N ( the set of natural numb...

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  20. intcos(logx)dx

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