calculus II

Question

Set up the definite integral that gives the area of the region.
y1 = x2 + 2x + 3
y2 = 2x + 19

Answer 1

Set the functions equal to each other get your bounds.  Since you have a quadratic function for one of them, you will have only two bounds.  Therefore, only one area under the curve.

 

Area under curve = ∫[(2x + 19) - (x² + 2x + 3)]dx

                          = ∫(16 - x²)dx

 

using the bounds.