Calculus question. Please help me with step by step.

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

Using Geometry (make and label a diagram!)

f(x) = mx + b

f(a₁) = ma₁ + b

f(a₂) = ma₂ + b

A = 0.5(ma₁ + b + ma₂ + b)(a₂ - a₁) It's a trapezoid!

A = 0.5(ma₁ + ma₂ + 2b)(a₂ - a₁)

Further simplification cannot be done.

Answer 2

Hi Sam,

The first step is to find an antiderivative of y = mx + b. Have you been able to do that?