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Let `f:RtoR` be a differentiable function having `f(2)=6,f'(2)=(1)/(48)`.Then `Lt_(x-2)int_(6)^(f(x))(4t^(3))/(x-2)dt`

A

24

B

36

C

12

D

18

Text Solution

Verified by Experts

The correct Answer is:
D
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AAKASH SERIES-DEFINITE INTEGRALS-EXERCISE - II
  1. Lt(xto0)(x^(2))/(int(0)^(x)Tan^(-1)tdt)

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  2. {:(" " Lt),(x rarr 0):} (int(0)^(x^(2))sec^(2) t dt)/(x sin x) =

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  3. Let f:RtoR be a differentiable function having f(2)=6,f'(2)=(1)/(48).T...

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  4. Let P(x) be a function defined on R such that P(x) = P'(1--x), AA x in...

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  5. If I(1) = int(1)^(2)(dx)/(sqrt(1+x^(2))) and I(2)= int(1)^(2) (dx)/(x)...

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  6. If I(1)= int(0)^(3pi) f( sin^(2) x)dx and I(2)= int(0)^(pi) f(sin^(2)x...

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  7. I= int(0)^(1)e^(x^(2))dx rArr

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  8. If I(1) = int(0)^(1) 2^(x^(2))dx, I(2) = int(0)^(1) 2^(x^(3))dx, I(3) ...

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  9. If [x] denotes the greatest integer less than or equal to x then int(1...

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  10. int(0)^(oo)[(2)/(e^(x))]dx=

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  11. Let I = int(0)^(1) (sin x)/(sqrt(x)) dx and J= int(0)^(1) (cos x)/(sqr...

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  12. Which of the following is true Statement-I : int(0)^(2pi) sqrt((1-cos2...

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  13. Which of the following are false : Statement-I : (int(0)^(pi//2) (sq...

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  14. Which of the following are true: I : int(0)^(4) sqrt(x^(2)-4x +4)dx=...

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  15. Arrange the following according to their values in ascending order A...

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  16. If 2 int(0)^(1) tan^(-1) x dx = int(0)^(1) cot^(-1) (1- x+x^(2))dx, th...

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  17. Arrange the following according to their values in ascending order A...

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  18. Match the following : {:(" LIST - I","LIST - II"),("I)" int(0)^(2)|...

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  19. If I(n) = int(0)^(pi//2) x^(n).cos x dx then the value of I(9)+72I(7)=

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  20. int(-pi//4)^(pi//4)((x+pi//4)/(2-cos2x))dx=

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