Evaluate the integral.

Question

2	f(x) dx
−3
where f(x) =	3	if	−3 ≤ x ≤ 0
6 − x2	if	0 < x ≤ 2

Answer 1

In this case, you have two segments of your piecewise function and you can separate them into two integrals:

∫⁰_-3 3•dx + ∫²₀ (6 - x²)dx

= [3x]⁰_-3 +[6x - (1/3)x³]²₀

= 3(0) - 3(-3) + 6(2) - (1/3)(2)³ - [6(0)-(1/3)(0)³]

= 9 +12 + (8/3)

=(27+36-8)/3

= 55/3

≈18.33