PLEASE HELP!!! I don't know the exact topic of this question but please help.

Question

Find the area under the graph of y=mx+b from x=a₁ to x=a₂ and verify your answer by using plane geometry. Assume that mx+b ≥ 0 on [a₁, a₂].

Answer 1

Sam, you are just taking the integral of y from a₁ to a₂.

For example, if y = 4x + 1, then an antiderivative of y is

F(x) = 2x² + x

The integral of y from 1 to 4 is

F(4) - F(1) = 32 + 1 = 33, which is the area under 4x + 1 from 1 to 4.