MTH 251- Midterm Exam Guide - Comprehensive Notes for the exam ( 25 pages long!)

• School: Miami University
• Department: Mathematics
• Course: MTH 251
• Professor: Konstantinos Beros

Document Summary

Mth251-lecture #1-review of syllabus and integration and introduction to integration by. Important points from the syllabus review: the textbook we will be using is calculus:early transcendentals, 8th edition by james. To find u, look for a function who"s derivative is also in the function. Because -2sin(2x) is also in the function, without the -2. Solving so that cancellation is possible: arctan (cid:4666)(cid:1876)(cid:4667)=tan (cid:2869)(cid:1876) Factor out the lowest power in the denominator (cid:1873)=(cid:4666)(cid:1876)(cid:2870)(cid:2871)+(cid:883)(cid:4667) (cid:1856)(cid:1873)=(cid:884)(cid:885)(cid:1876) (cid:2869)(cid:2871)(cid:1856)(cid:1876) (cid:885)(cid:884)(cid:1876)(cid:2869)(cid:2871)(cid:1856)(cid:1873)=(cid:1856)(cid:1876) (cid:1876)(cid:2869)(cid:2871) cancels. (cid:883)(cid:1876)+(cid:1876)(cid:2869)(cid:2871)(cid:1856)(cid:1876) (cid:1867)(cid:1870) (cid:883)(cid:1876)+ (cid:1876)(cid:3119) (cid:1856)(cid:1876) (cid:3117)(cid:3119)(cid:4666)(cid:3118)(cid:3119)+(cid:2869)(cid:4667)(cid:1856)(cid:1876) (cid:2869) (cid:883) (cid:1876)(cid:2869)(cid:2871)((cid:1876)(cid:2870)(cid:2871)+(cid:883))(cid:4666)(cid:885)(cid:884)(cid:1876)(cid:2869)(cid:2871)(cid:1856)(cid:1873)(cid:4667) We know from the product rule that (cid:3031)(cid:3031)[(cid:1858)(cid:4666)(cid:1876)(cid:4667)(cid:1859)(cid:4666)(cid:1876)(cid:4667)]=(cid:1858) (cid:4666)(cid:1876)(cid:4667)(cid:1859)(cid:4666)(cid:1876)(cid:4667)+(cid:1859) (cid:4666)(cid:1876)(cid:4667)(cid:1858)(cid:4666)(cid:1876)(cid:4667) Going to end up with a u, du, v, and dv. Look for something you can integrate for dv and something that can be made simpler by taking the derivative for u. Remember, you can always check your integrals using differentiation. (cid:1864)(cid:1866)|(cid:1876)| must be u because it can not be (cid:1856)(cid:1873)=(cid:883)(cid:1876)(cid:1856)(cid:1876),(cid:1874)=(cid:1876) integrated (cid:1871)(cid:1865)(cid:1868)(cid:1864)(cid:1858)(cid:1877) (cid:1873)(cid:1871)(cid:1866)(cid:1859),(cid:1876)((cid:883)(cid:1876))=(cid:883) This integral is one to know off hand: