Mathematics 134 – Intensive Calculus for Science 2 Discussion 3 – Some interesting integrals! Wednesday January 31, 2001

Background

Today, we want to practice using the substitution method to evaluate some indefinite integrals. Instead of writing up a set of solutions to be handed in, each group will put their work on the blackboard, and we will discuss the answers as a group. Group 5 A) Use the substitution u = x^{2} + 1 to evaluate

∫ 4x(x^{2} + 1) dx

B) Evaluate

∫ \frac{cos(\sqrt{t})}{\sqrt{t}} dt

by an appropriate substitution. C) There is a trig identity that says

sin(x) cos(x) = \frac{1}{2} sin(2x)

Use this, and an appropriate substitution to evaluate ∫ sin(x) cos(x) dx