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Let d/(dx) (F(x))= e^(sinx)/x, x>0. If ...

Let `d/(dx) (F(x))= e^(sinx)/x, x>0`. If `int_1^4 2e^sin(x^2)/x dx = F(k)-F(1)`, then possible value of k is:

A

4

B

8

C

16

D

32

Text Solution

Verified by Experts

The correct Answer is:
C
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ARIHANT MATHS-DEFINITE INTEGRAL-Exercise For Session 5
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  2. the value of int(0)^([x]) dx (where , [.] denotes the greatest integer...

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  3. Evaluate: int(-pi/4)^(npi-pi/4)|sinx+cosx|dx

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  4. Let f (x) = x – [x], for every real number x, where [x] is the greates...

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  5. f(x)=int0^xf(t)dt=x+intx^1tf(t)dt ,t h e nt h ev a l u eoff(1)i s 1/2...

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  6. The least value of the function phi(x)=overset(x)underset(5pi//4)int...

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  7. The poins of extremum of phi(x)=underset(1)overset(x)inte^(-t^(2)//2)...

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  8. If f(x) is periodic function with period, T, then

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  9. Let d/(dx) (F(x))= e^(sinx)/x, x>0. If int1^4 2e^sin(x^2)/x dx = F(k)...

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  10. Let f:(0,oo)to R and F(x)=int(0)^(x) f(t)dt. " If " F(x^(2))=x^(2)(1+x...

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  11. Let T >0 be a fixed real number. Suppose f is continuous function such...

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  12. Let f(x)=int1^xsqrt(2-t^2)dtdot Then the real roots of the equation , ...

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  13. Let f(x) be an odd continuous function which is periodic with period...

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  14. Let f(x) be a function defined by f(x)=int1^xt(t^2-3t+2)dt,1<=x<=3 The...

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  15. The value of lim(x rarr0)(2int(0)^(cos x ) cos^(-1) (t))/(2x- sin 2 x)...

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  16. If underset(0)overset(x)int (bt cos 4 t - a sin 4t)/( t^(2))dt=(a sin ...

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  17. If f(x)=int0^x{f(t)}^(- 1)dt and int0^1{f(t)}^(- 1)=sqrt(2), then

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  18. Let f be a real-valued function defined on the inverval (-1,1) such th...

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  19. Concider the function defined on [0,1] rarr R f(x) =(sinx- cosx)/(x^(2...

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  20. Concider the function defined on [0,1] rarr R f(x) =(sinx- cosx)/(x^(2...

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