Given the function graphed below, evaluate the definite integrals.

Question

∫²₀ f(x)dx = ∫⁷₂ f(x)dx =

Answer 1

x value of the first inegral can be found using the formula for area of a trapezoid with one base 2, (0, 2) and the other 3 (2, 3) with the height being 2.

In the second inegral the area from x = 2 to x = 3 is equal to an opposite that of the area from x = 3 to x = 4. Value is 0 (zero).

The remaining area is a rectangle that is 3 (7 - 4) by 3 (0 - 3).