Home
Class 12
MATHS
If f(a+b-x)=f(x), then inta^b x f(x)dx i...

If `f(a+b-x)=f(x)`, then `int_a^b x f(x)dx` is equal to (A) `(a-b)/2int_a^b f(a+b-x)dx` (B) `(a+b)/2int_a^b f(b-x)dx` (C) `(a+b)/2int_a^b f(x)dx` (D) `(b-a)/2int_a^b f(x)dx`

A

`(a+b)/2 int_a^b f(b-x)dx`

B

`(a+b)/2 int_a^b f(b+x) dx`

C

`(b-a)/2 int_a^b f(x) dx`

D

`(a+b)/2 int_a^b f(x) dx`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • INTEGRALS

    MODERN PUBLICATION|Exercise FILL IN THE BLANKS|15 Videos

  • INTEGRALS

    MODERN PUBLICATION|Exercise TRUE/FALSE QUESTIONS|10 Videos

  • INTEGRALS

    MODERN PUBLICATION|Exercise SUB CHAPTER 7.3 EXERCISE 7(p) LONG ANSWER TYPE QUESTIONS (I)|12 Videos

  • DIFFERENTIAL EQUATIONS

    MODERN PUBLICATION|Exercise CHAPTER TEST (9)|12 Videos

  • INVERSE - TRIGONOMETRIC FUNCTIONS

    MODERN PUBLICATION|Exercise CHAPTER TEST (2)|11 Videos

Similar Questions

Explore conceptually related problems

If (2a+2b-x)=f(x), then int_(2a)^(2b)xf(x)dx is equal to

If f(x)=f(a+b-x), then int_(a)^(b) xf(x)dx is equal to

If f(a+b-x)=f(x) , then inta bf(x)dx is equal to (A) (a+b)/2inta bf(b-x)dx (B) (a+b)/2inta bf(b+x)dx (C) (b-a)/2inta bf(x)dx (D) (a+b)/2inta bf(x)dx

If f(a+b-x)=f(x),\ t h e n\ int_a^b xf(x)dx is equal to (a+b)/2int_a^bf(b-x)dx b. (a+b)/2int_a^bf(b+x)dx c. (b-1)/2int_a^bf(x)dx d. (a+b)/2int_a^bf(x)dx

int_a^b[d/dx(f(x))]dx

If f(a+b-x)=f(x),\ then prove that \ int_a^b xf(x)dx=(a+b)/2int_a^bf(x)dx

If f(a+b-x0=f(x) , then prove that int_a^b xf(x)dx=((a+b)/2)int_a^bf(x)dxdot

If f(a+b-x)=f(x), then prove that int_(a)^(b)xf(x)dx=(a+b)/(2)int_(a)^(b)f(x)dx

int_0^a[f(x)+f(-x)]dx= (A) 0 (B) 2int_0^a f(x)dx (C) int_-a^a f(x)dx (D) none of these