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Let (d)/(dx) F(x)=(e^(sin x))/(x), x gt...

Let `(d)/(dx) F(x)=(e^(sin x))/(x), x gt 0`,
If `int_(1)^(4) (3)/(x) e^(sin x^(3))dx=F(k)-F(1)`, then one of the possible value of k is -

A

15

B

16

C

63

D

64

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The correct Answer is:
D
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MOTION-DEFINITE INTEGRATION -EXERCISE -2 (LEVEL-I)
  1. If underset(0)overset(oo)int e^(-x^(2))dx=sqrt((pi)/(2))"then"underset...

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  2. Let A = underset(0)overset(1)int(e^(t))/(1+t) dt, then underset(a-1)ov...

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  3. Let (d)/(dx) F(x)=(e^(sin x))/(x), x gt 0, If int(1)^(4) (3)/(x) ...

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  4. 1/c int (a) ^(b) f ((x)/(c )) dx =

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  5. int(5/2)^5 (sqrt((25-x^2)^3))/(x^4) dx

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  6. If {:(f(x)=x", ...."x lt 1),(" "=x-1", ...." x ge 1","):} ...

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  7. Suppose for every integer n, . underset(n)overset(n+1)intf(x)dx = n^(2...

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  8. int (0) ^(pi) (1 + 2 cos x ) dx equal to :

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  9. The value of int (-1) ^(3) (|x-2 |+[x]) dx is equal to (where [**] den...

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  10. If underset(-1)overset(3//2)int|xsinpix|dx = (k)/(pi^(2)), then the va...

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  11. int0^(10pi) |sin x| dx is

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  12. The value of int (-1) ^(3) | 1- x ^(2) | dx is -

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  13. rArrunderset(0)overset(oo)int[(2)/(e^(x))]dx (where [*] denotes the gr...

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  14. int0^sqrt2 [x^2]dx

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  15. If f (x) = int (0) ^(x) sin [2x] dx then f ( pi//2) is (where [**] de...

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  16. f(x)=Minimum{tanx,cotx}AA x in(0,pi/2) Then int0^(pi/3)f(x)dx is equal...

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  17. The value of int (1) ^(2) ([x ^(2) ]- [x] ^(2) dx is equal to (where [...

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  18. If f(x)={e^(cosxsinx ,for|x|lt=2)2,ot h e r w i s e ,t h e nint(-2)^3f...

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  19. The value of int0^(pi/3) [sqrt3 tanx]dx( where [.] denotes the greates...

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  20. T h ev a l u eofint(-2)^1[x[1+cos((pix)/2)]+1]dx , where [.] denotes ...

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