Use the formula for the area of a trapezoid to evaluate ∫42(2x+3)dx.

Question

I know the area of a trapezoid is ((a+b)/2)*h but idk what's what....please help!

Answer 1

Draw or graph the function, and you will see that you have a trapezoid. The 4 sides of the trapezoid are y = 0, y = 2x+3, x = x_min, and x = x_max , where xmin and xmax are the endpoints for the interval over which we integrate.

Then, we can plug into your formula

h = x_max - x_min

a = 42(2x_min + 3)

b = 42(2x_max + 3)