Graph the integrand and use known area formulas to evaluate the integrals.

Question

Graph the integrand and use known area formulas to evaluate the integrals.

∫-1 to 1 (1-abs(x))dx

Answer 1

f(x) = 1 - |x| is the same as f(x) = -|x| + 1 meaning the "v-shaped" parent function (y = |x|) is reflected over the x-axis and moved up by 1 unit:

The shaded portion is the area under the curve which is equivalent to the noted integral.

This is a triangle whose area is defined as:

A = (1/2)bh where b = 2 and h = 1