Find the area (in square units) of the region under the graph of the function f on the interval [−3, 5], using the Fundamental Theorem of Calculus. Then verify your result using geometry.

Question

f(x)=6

Find the area (in square units) of the region under the graph of the function f on the interval [−3, 5], using the Fundamental Theorem of Calculus. Then verify your result using geometry.

Answer 1

Area, A = ∫_-3⁵ 6 dx = 6t |_-3⁵ = 30 - (-18) = 48 units²

This is a rectangle of height 6 and a width of 5 - (-3) = 8

A = 8·6 = 48 units²