Mathematics 0110A/B Study Guide - Quiz Guide: Antiderivative, Thx, Riemann Sum

• School: Western University
• Department: Mathematics
• Course: Mathematics 0110A/B
• Professor: Chris Brandl

Document Summary

Topics: antiderivatives, de nite/inde nite integrals, substitution rule, riemann sums, and approximate integration. Any outright copying of assignments will be reported as an act of academic plagiarism. (cid:90) (cid:32: find the following antiderivatives. (a) tan2(x) + x 3. 2 + x + 2 x2 dx (cid:33) Since we do not readily know the antiderivative of tan2(x) we use the trig identity tan2(x) + 1 = sec2(x). Using the identity and simplifying we get tan2(x) + x 3. From this we see that (cid:90) (cid:32) tan2(x) + x 3. 2 + x + 2 x2 (cid:19) dx sec2 (x) 1 + 2 x2 x + ln|x| 2 x. From this we see that(cid:90) 1 + sin3(x) (cid:90) sin2(x) = csc2 (x) + sin (x) (cid:90) (cid:0)csc2 (x) + sin (x)(cid:1) dx dx = = cot (x) cos (x) + c (c) dx . Let u = x 1, we get that du = dx. 1 u2 (cid:90) (d) e2x ex 1.