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Let f:(0,oo)to R and F(x)=int(0)^(x) f(t...

Let `f:(0,oo)to R and F(x)=int_(0)^(x) 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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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 ever real number x ,w h e r e[x] is the g...

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  5. If int0^x f(t) dt=x+intx^1 tf(t)dt, then the value of f(1) is

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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) ,xgt0. If int (1)^(4)(2e^(sinx2))/(x)d...

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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)dt Then the real roots of the equation x^2-f...

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  13. The points of extremum of phi (x)=int(1)^(x)e^(-t^(2//2)) (1-t^(2)) dt...

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  14. Let f:[2, infty) to R be the function defined by f(x)=x^(2)-4x+5, then...

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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. Consider the function defined on [0,1] rarr R , f(x) =(sinx- xcosx)/(x...

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  20. Evaluate int (0)^(2) x^3 dx

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