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Let `f:(0, oo) in R and F(x) =underset(0)overset(x) int f(t) dt`. If `F(x^(2))=x^(2)(1+x)` then f (4) equals

A

`(5)/(4)`

B

7

C

4

D

2

Text Solution

Verified by Experts

The correct Answer is:
C
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ML KHANNA-DEFINITE INTEGRAL-Problem set (5) (Multiple Choice Questions)
  1. If int(sin x)^(1) t^(2) f(t) dt =1- sin x, x in (0, (pi)/(2)) then f((...

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  2. If f(x)= int(x^(2))^(x^(3)) (dt)/(log t), x gt 0 then

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  3. Let f:(0, oo) in R and F(x) =underset(0)overset(x) int f(t) dt. If F(x...

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  4. If int(0)^(t^(2)) xf (x) dx= (2)/(5) t^(5), then f(4/25)=

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  5. The integral int(0)^(2) (|x+2|)/(x+2)dx is equal to

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  6. int(-3)^(3) (x-4)/((|x-4|))dx=

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  7. The value of overset(sin^(2)x)underset(0)int sin^(-1)sqrt(t)dt+overs...

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  8. If int(pi//3)^(x) sqrt(3-2sin^(2)u) du + int(0)^(y) cos t dt= 0, then ...

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  9. The points of extremum of the function F(x)= int(1)^(x) e^(-t^(2)) (1-...

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  10. The points of extemum of f(x)= int(0)^(x^(2)) (t^(2)- 5t +4)/(2+e^(t))...

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  11. If int(0)^(x) f(t) dt= x + int(x)^(1) t f(t) dt, then the valeu of f(1...

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  12. If int(0)^(t) (bx cos 4x- a sin 4x)/(x^(2)) dx= (a sin 4t)/(t)-1, wher...

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  13. Lt(x rarr 0)(int(0)^(x^(2)) (tan^(-1) t)^(2) dt)/(int(0)^(x^(2)) (sin ...

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  14. The value of the integral overset(b)underset(a)int (|x|)/(x)dx, a lt b...

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  15. If a lt 0 lt b, then int(a)^(b) x|x| dx=

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  16. int (-1)^(1)| 1 - x| dx is equal to

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  17. int(-2)^(2) |x(x-1)|dx=

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  18. int(0)^(4) |x-1| dx=

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  19. The vaue of underset(-1)overset(2)int (|x|)/(x)dx is

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  20. int(0)^(2) |(1-x)|dx=

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