The function is to be integrated over the interval

MATHEMATICS · Multi-part · AP · Calculus BC · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

The function

q(x)=\dfrac{4x-7}{(x-3)(x+1)}

is to be integrated over the interval

[0,4]

. Let

M=\displaystyle \int_{0}^{4} q(x)\,dx

. (1) Part 1: Express

M

as one or more limits of definite integrals whose integrands are continuous on their respective intervals. (2) Part 2: Determine whether

M

converges. Provide a clear justification that references the limit(s) written in part (a). (3) Part 3: If

M

converges, evaluate it exactly; if it diverges, state the type of divergence and support your conclusion.