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

Let `(d)/(dx) F (x) = (e^(sin x))/(x), x gt 0`. If `int_(1)^(4) (2xe^(sin x^(2)))/(x^2) dx= F(k)-F(1)` then one of the possible value of k is

A

4

B

16

C

2

D

none

Text Solution

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The correct Answer is:
B
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ML KHANNA-DEFINITE INTEGRAL-ProblemSet (1) (Multiple Choice Questions)
  1. If int(-2)^(3) f (x) dx= 5 and int(1)^(3) [2-f(x)] dx=6, then int(-2)^...

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  2. If int(-1)^(4) f(x) dx= 4 and int(2)^(4) [3-f(x)] dx= 7, then the valu...

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  3. The value of the integral Sigma(r=1)^(n) int(0)^(1) f(r-1 +x) dx is

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  4. The value of int(0)^(100) e^(x- [x])dx is

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  5. If f(x) is a function satisfying f((1)/(x)) + x^(2) f(x) =0 for all no...

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  6. If 2f(x) + 3f((1)/(x))= (1)/(x)-2, x ne 0 then int(1)^(2) f(x)dx=

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  7. The value of the integral int(0)^(oo) (x log x)/((1+x^(2))^(2)) dx is

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  8. int(0)^(1) "tan"^(-1) (2x-1)/({1+x-x^(2)})dx=

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  9. The value of int(1//e)^(tan x) (t)/(1+ t^(2)) dt+ int(1//e)^(cot x) (1...

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  10. int(0)^(pi) sin^(5) ((x)/(2))dx equals

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  11. If int(0)^(pi//2) cos^(m) x sin^(m) x dx= lamda int(0)^(pi//2) sin^(m)...

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  12. The value of int(1)^(e^(37)) (pi sin (pi ln x))/(x) dx is

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  13. If int(-2)^(5) f(x) dx= 7.5^(3)- 7(-2)^(3) then f(x) is equal to

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  14. Let (d)/(dx) F (x) = (e^(sin x))/(x), x gt 0. If int(1)^(4) (2xe^(sin ...

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  15. Let (d)/(dx)F (x)= (e^(sin x))/(x), x gt 0. If int(1)^(4) (3x^2)/(x^3)...

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  16. (1)/(c ) int(a c)^(bc) f((x)/(c ))dx=

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  17. If A= int(0)^(1) (dx)/(sqrt(1+x^(4))) and B= (pi)/(4) then

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  18. If g(x)=int(0)^(x)cos^(4) t dt , then g(x+pi) equals

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  19. int(-a)^(a) f (x) dx is equal to

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  20. int(1//2)^(2) |log(10) x| dx=

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