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Let f(x) be a continuous function such t...

Let f(x) be a continuous function such that f(a-x)+f(x)=0 for all ` x in [0,a]`. Then, the value of the integral
`int_(0)^(a) (1)/(1+e^(f(x)))dx` is equal to

A

a

B

`(a)/(2)`

C

f(a)

D

`(1)/(2)f(a)`

Text Solution

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The correct Answer is:
B
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OBJECTIVE RD SHARMA-DEFINITE INTEGRALS-Exercise
  1. int(-pi/2)^(pi//2) log(e ){((ax^(2)+bx+c)/(ax^(2)-bx+c))(a+b)|sinx|}dx...

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  2. For any natural number n, the value of the integral int(0)^(sqrt(n))...

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  3. For any n in R^(+), the value of the integral int(0)^(n[x]) (x-[x])d...

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  4. If phi'(x)=(log(e )|sin x|)/(x),x ne pi,n in Z and int(1)^(3) (3log(...

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  5. The equation int(-pi//4)^(pi//4) {a|sin x|+(b sin x)/(1+cos x)+c}dx=...

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  6. Let f(x) be a continuous function such that f(a-x)+f(x)=0 for all x i...

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  7. The value of int(alpha)^(beta) x|x|dx, where a lt 0 lt beta, is

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  8. int(-pi//2)^(pi//2) (|x|)/(8 cos^(2)2x+1)dxhas the value

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  9. If [.] denotes the greatest integer function and f(x)={:{(3[x]-(5|x|...

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  10. Find the value of int(-1)^1[x^2+{x}]dx ,w h e r e[dot]a n d{dot} denot...

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  11. The value of int(-1)^(1)sin^(-1)[x^(2)+(1)/(2)]dx+int(-1)^(1) cos^(-...

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  12. Let Delta(y)=|{:(y+a,y+b,y+a-c),(y+b,y+c,y-1),(y+c,y+d,y-b+d):}| and,...

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  13. If I=int0^(1) (1)/(1+x^(pi//2))dx, then\

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  14. If int(0)^(x) f(t)dt=x^(2)+2x-int(0)^(x) tf(t)dt, x in (0,oo). Then, f...

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  15. The value of int(-6)^(6) "max"(|2-|x||,4-|x|,3)dx ,is

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  16. If I(n)=int(0)^(pi) e^(x)(sinx)^(n)dx, then (I(3))/(I(1)) is equal to

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  17. Given that lim(n to oo)sum(r=1)^(n)(log(n^(2)+r^(2))-2logn)/(n)=log2...

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  18. Let f(x)be a differentiable function such that f'(x)=f(x)+int(0)^(2)...

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  19. Let f(x) be a differentiable function satisfying f'(x)=f(x)+int(0)^(2)...

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  20. The value of the integral int(-10)^(0) (|(2[x])/(3x-[x])|)/(((2[x])/(3...

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