21 Integration by Substitution: Problem 1 (10 points) Consider the integral f 5zt (m5 oty 1) dz. In the following, we will evaluate the integral using two methods. A. First, rewrite the integral by multiplying out the integrand: /5&4(3:5 +1)dz = [ E]da': Then evaluate the resulting integral term-by-term: /5&4@5 +1) dz =O B. Next, rewrite the integral using the substitution w = 2% +1; / bzt (2 4 1)dz = f E]dw Evaluate this integral (and back-substitute for w) to find the value of the original integral: /5$4(w5+1)d$=0 C. How are your expressions from parts (A) and (B) different? What is the difference between the two? (answer from B) (answer from A) = Are both of the answers correct? 21 Integration by Substitution: Problem 2 (8 points) Find the following indefinite integral (antiderivative). In' (z) dz = Z\fFind the indefinite integral (antiderivative). sin( -2x) da =\f(8 points) Evaluate the integral. e2t e-2t e2* + e-2t dt = Hint: Try substitution with u = e + e-2t