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Let f: R rarr R be a continuous function...

Let `f: R rarr R `be a continuous function given by `f(x+y)=f(x)+f(y)` for all `x,y, in R,` if `int_0^2 f(x)dx=alpha,` then `int_-2^2 f(x) dx` is equal to

A

`2 alpha`

B

` alpha`

C

0

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
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ARIHANT MATHS-DEFINITE INTEGRAL-Exercise For Session 4
  1. Let f: RvecR a n d g: RvecR be continuous function. Then the value of ...

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  2. The value of int(-1)^(1)(x|x|)dx is equal to

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  3. The value of int(-1)^(1)((x^(2)+ sin x)/(1+x^(2)))dx is equal to

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  4. If f is an odd function, then the value of int(-a)^(a)(s(sinx))/(f(cos...

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  5. Evaluate: int-(1/sqrt(3))^(1/sqrt(3)) (cos^-1((2x)/(1+x^2))+tan^-1((2x...

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  6. Find the value of int(-pi)^(pi)(cos^(2)x)/(1+a^(x))dx, agt0.

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  7. The integral int(-1/2)^(1/2) ([x]+1n((1+x)/(1-x)))dx is equal to (wher...

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  8. Evaluate: int(-pi//2)^(pi//2)1/(1+e^(sin x))dx

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  9. If [*] denots the greatest integer function then the value of the inte...

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  10. The equation int(-pi/4)^(pi/4){a|sinx|+(bsinx)/(1+cos^2x)+c}dx=0 where...

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

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  12. Let f(x) be a contiuous function such a intn^(n+1) f(x)dx=n^3, n in Z...

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  13. Let f(x)=(e^(x)+1)/(e^(x)-1) and int(0)^(1) x^(3) .(e^(x)+1)/(e^(x)-1)...

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  14. Let f: R rarr R be a continuous function given by f(x+y)=f(x)+f(y) for...

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  15. The value of int(-2)^(2) x dx is equal to

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  16. Find the second order derivative if y= e^(2x)

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  17. Let f(x)={1-|x|,|x| leq 1 and 0,|x| lt 1 and g(x)=f(x-1)+f(x + 1), fo...

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  18. If int(n)=int(-pi)^(pi)(sin nx)/((1+pi^(x))sinx) dx, n=0,1,2,………. then

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  19. Let I(n)=int(-pi)^(pi)(sin x)/((1+pi^(x))sin x )dx, n=0,1,2,... The va...

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  20. Let I(n)=int(-pi)^(pi)(sin x)/((1+pi^(x))sin x )dx, n=0,1,2,... The va...

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