The function q(x)=(x−3)(x+1)4x−7 is to be integrated over the interval [0,4]. Let M=∫04q(x)dx.
a. Part 1: Express M as one or more limits of definite integrals whose integrands are continuous on their respective intervals.
b. Part 2: Determine whether M converges. Provide a clear justification that references the limit(s) written in part (a).
c. Part 3: If M converges, evaluate it exactly; if it diverges, state the type of divergence and support your conclusion.