If f(a + b - x) = f(x), then ∫ba xf (x) dx is equal to:

Question

If f(a + b - x) = f(x), then ∫ba xf (x) dx is equal to: (A) (a +b/2) ∫ba f(b - x)dx (B) (a +b/2) ∫ba f( x)dx (C) (b - a /2) ∫ba f( x)dx (D) none of these

Tardigrade Admin · Accepted Answer

Given f(a + b - x) = f(x) ⇒ a +b - x = x ⇒ x = (a + b/2) Let I = ∫ba xf (x) dx = (a+ b/2) ∫ba f(x) dx

Q. If $f (a + b - x) = f (x),$ then $\int_{a}^{b} x f (x) d x$ is equal to:

$\frac{a + b}{2} \int_{a}^{b} f (b - x) d x$

$\frac{a + b}{2} \int_{a}^{b} f (x) d x$

$\frac{b - a}{2} \int_{a}^{b} f (x) d x$

none of these

Given f(a + b - x) = f(x)
$\Rightarrow a + b - x = x \Rightarrow x = \frac{a + b}{2}$
Let $I = \int_{a}^{b} x f (x) d x = \frac{a + b}{2} \int_{a}^{b} f (x) d x$

Q. If f(a+b−x)=f(x), then ∫ab​xf(x)dx is equal to:

2a+b​∫ab​f(b−x)dx

2a+b​∫ab​f(x)dx

2b−a​∫ab​f(x)dx