MATHEMATICS · Multi-part · AP · Calculus BC · Integration and Accumulation of Change · Integration and Accumulation of Change
Problem
Consider the function
g(x)=(x−2)(x+3)5x+1.
Let I=∫05g(x)dx.
(1) Part 1: Identify all x–values in the interval [0,5] at which g(x) is not defined.
(2) Part 2: Determine whether I is a proper or an improper integral. If it is improper, clearly indicate the point(s) that create the improper behavior and explain why.
(3) Part 3: Rewrite I, if needed, as one or more limit expressions that must be evaluated in order to find its value. (Do not evaluate the limits.)
(4) Part 4: Without performing any integration, state whether the antiderivative of g(x) is expected to involve natural logarithm terms, inverse–trigonometric terms, or both. Justify your answer based on the algebraic structure of g(x).