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If f(x)=int(x)^(-1) |t|dt, then for any...

If f(x)`=int_(x)^(-1) |t|dt`, then for any `x ge 0`, f(x) equals

A

`(1)/(2)(1-x^(2))`

B

`(1)/(2)x^(2)`

C

`(1)/(2)(1-x^(2))`

D

none of these

Text Solution

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The correct Answer is:
C
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OBJECTIVE RD SHARMA-DEFINITE INTEGRALS-Chapter Test 1
  1. The greater value of (x)=int(-1//2)^(x) |t|dt on the interval [-1//2,1...

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  2. f(x)={:{(1-x","" "0 le c le 1),(0","" "1 le x le 2" and "phi ...

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  3. If f(x)=int(x)^(-1) |t|dt, then for any x ge 0, f(x) equals

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  4. int0^(2) (x-log(2)a)dx=2 log((2)/(a)), if

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  5. If int(1)^(a) (a-4x)dx ge 6-5a, a gt 1, then a equals

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  6. The value of int1^2 {f(g(x))}^(-1)f'(g(x))g'(x) dx , where g(1)=g(2),...

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  7. If C0/1+C1/2+C2/3=0 , where C0 C1, C2 are all real, the equation C2x...

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  8. The solution of the equation int(log(2))^(x) (1)/(e^(x)-1)dx=log(3)/(2...

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  9. If int(a)^(b) (x^(n))/(x^(n)+(16-x)^(n))dx=6, then

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  10. Let m be any integer. Then, the integral int(0)^(pi) (sin 2m x)/(sin x...

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  11. int(-pi//4)^(pi//4) e^(-x)sin x" dx" is

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  12. (d)/(dx)(f(x))=phi(x)" for "a lex le b,int(a)^(b) f(x)phi(x)dx=

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  13. int(-pi//2)^(pi//2) (cos x)/(1+e^(x))dx=

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  14. int(0)^(oo) (dx)/([x+sqrt(x^(2)+1)]^(3))dx=

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  15. int(0)^(oo) (x)/(1-x)^(3//4)dx=

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  16. int(0)^(pi) xsin x cos^(4)x dx=

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  17. int(0)^(pi) [2sin x]dx=

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  18. int(pi//2)^(3pi//2) [2cos x]dxis equal to

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  19. If f(x) satisfies the conditions of Rolle's theorem in [1,2] and is co...

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  20. For y=f(x)=int(0)^(x) 2|t|dt, the tangent lines parallel to the bi-sec...

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