Home
Class 12
MATHS
If f(a+b-x)=f(x),\ t h e n\ inta^b xf(x)...

If `f(a+b-x)=f(x),\ t h e n\ int_a^b xf(x)dx` is equal to
a.`(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`

Text Solution

Verified by Experts

Given` f(a + b - x) = f(x)`
⇒`a+b−x=x`
⇒`x=(a+b)/2​`
Let` I=∫_a^babf(x)dx =(a+b)/2∫_a^babf(x)dx`
Hence option D is correct
Promotional Banner

Topper's Solved these Questions

  • INTEGRALS

    NCERT ENGLISH|Exercise EXERCISE 7.3|24 Videos

  • INTEGRALS

    NCERT ENGLISH|Exercise SOLVED EXAMPLES|46 Videos

  • INTEGRALS

    NCERT ENGLISH|Exercise EXERCISE 7.5|23 Videos

  • DIFFERENTIAL EQUATIONS

    NCERT ENGLISH|Exercise EXERCISE 9.1|12 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    NCERT ENGLISH|Exercise Solved Examples|13 Videos

Similar Questions

Explore conceptually related problems

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

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

int_(a)^(b) 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

int_(a+c)^(b+c) f(x) dx is equal to

int_a^b logx/x dx

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

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

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

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