MATH 2B Lecture Notes - Lecture 7: Antiderivative

• School: UC-Irvine
• Department: Mathematics
• Course: MATH 2B
• Professor: Kenn Huber

Document Summary

Math 2b - lecture 7 6. 1: area between curves. Let"s say we are given a graph and are asked to find the are in between the two curves. Well, from previous lessons, we know that finding the area gives us the anti-derivative of a function, so we will be taking the anti-derivative using definite integrals here. (cid:1857)(cid:1853)= (cid:4666)(cid:1867)(cid:1868) (cid:1854)(cid:1867)(cid:1867)(cid:1865)(cid:4667) (cid:1856)(cid:1876) (cid:3029) (cid:3028) Thus, our equation for the graph would be (cid:1857)(cid:1853)= [(cid:1858)(cid:4666)(cid:1876)(cid:4667) (cid:1859)(cid:4666)(cid:1876)(cid:4667)] (cid:1856)(cid:1876) (cid:1877)=(cid:1876)(cid:2870),(cid:1877)=(cid:884)(cid:1876) Let"s say that the intervals were not shown on the graph. Well, the interval starts and ends at the point of intersections, so we would set the y- equations equal to each other. (cid:1876)(cid:2870)=(cid:884)(cid:1876) (cid:1876)(cid:4666)(cid:1876) (cid:884)(cid:4667)=(cid:882) (cid:1876)=(cid:882),(cid:884) Now, that we have our interval, we can use the equation above to find the area. (cid:2870) Find the area enclosed by all three functions. This ti(cid:373)e, let"s try o(cid:374)e where doi(cid:374)g top bottom might be a bit more challenging. (cid:1876)=(cid:1877)(cid:2870), (cid:1877)=(cid:884) (cid:1876)