CAS MA 124 Study Guide - Midterm Guide: Power Rule, Partial Fraction Decomposition

• School: Boston University
• Department: Mathematics & Statistics
• Course: CAS MA 124
• Professor: All

Document Summary

Ma 124 - spring 10 - exam 1 - prof. meuser: (16 points) find the derivative of f(x) = (cid:90) 0 ex tan3 t dt. State any rules and theorems you are applying and where you are applying them. Answer: (cid:90) a f(x) dx = f(x) dx (cid:90) ex b f(x) = tan3 t dt. 0 f(x) = f(u) = tan3 t dt (cid:90) b a (cid:90) u. By the fundamental theorem of calculus i we have. Since u = ex , du/dx = ex. = tan3 u ex = ex tan3 ex: (16 points) find the values of the following de nite integrals. Simplify your answers as much as possible: (8 points) (cid:90) 1. Then du = 3dx so (1/3)du = dx. When x = 0 , u = 1 and when x = 1 , u = 2. Integrating using the power rule we get (cid:90) 1. 1 (3x 1)49 dx = u49 du =