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

If `f(x)=int_(-1)^(x)|t|dt`, then for any `xge0,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

Verified by Experts

The correct Answer is:
C
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OBJECTIVE RD SHARMA ENGLISH-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(-1)^(x)|t|dt, then for any xge0,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. If (d(f(x)))/(dx) = g(x) AA x in [a, b] then int(a)^(b)f(x).g(x)dx is ...

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  13. Evaluate : int(-pi/2)^(pi/2)(cosx)/(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)^(1) (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 condition of Rolles theorem in [1, 2] then int1^...

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  20. The tangent lines for the curve y=int(0)^(x)2|t|dt which are parallel ...

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