1.Define the real valued function f(x) = |x^2 + 2x – 3| 2. Evaluate ∫|x^2 + 2x – 3|dx. x ∈ [0,2]

Question

1. Define the real valued function f(x) = |x² + 2x – 3| 
2. Evaluate \(\int\limits_0^2\)|x² + 2x – 3|dx.

Answer 1

1. f(x) = |x² + 2x – 3| = |(x – 1) (x + 3)|

We have;

2. I = \(\int\limits_0^2\)|x² + 2x – 3|dx