Integration of absolute value function.. please help

**kokoro123** · June 7th 2012, 07:03 AM

Let f(a) = S₀²|x(x-a)| dx for 0< a <

(1) Find the function f(a).

(2) Find the minimum of f(a).

Thank you very much for your help!

**Plato** · June 7th 2012, 07:14 AM

Originally Posted by kokoro123

Let f(a) = S₀²|x(x-a)| dx for 0< a <

(1) Find the function f(a).

(2) Find the minimum of f(a).

The integral becomes $\int_0^a {x(a - x)dx} + \int_a^2 {x(x - a)dx}$

**Reckoner** · June 7th 2012, 07:14 AM

Originally Posted by kokoro123

(1) Find the function f(a).

Originally Posted by kokoro123

(2) Find the minimum of f(a).

Use the Fundamental Theorem of Calculus to differentiate $f$ . Locate critical values, etc.

Thread: Integration of absolute value function.. please help