MAT137Y5 Chapter Notes - Chapter integration: Equilateral Triangle, Ellipse

• School: UTM
• Department: Mathematics
• Course: MAT137Y5
• Professor: Ali Mousavidehshikh

Document Summary

Olids of (cid:396)e(cid:448)olutio(cid:374) is a (cid:272)ool (cid:449)a(cid:455) to i(cid:374)teg(cid:396)ate (cid:858)si(cid:373)ple(cid:859) (cid:1007)d shapes (cid:449)ho ha(cid:448)e a good (cid:396)elatio(cid:374) to (cid:272)i(cid:396)(cid:272)les. Fo(cid:396) an idea of this, think of the torus. The torus could be thought of the area of a circle, times a circle (i. e. (cid:1870)(cid:2870) (cid:884)(cid:1870)). using the solids of revolution technics that i will show later, this will be shown to indeed be the case by starting with. Which could easily be represented as two equations. This saves us from using multi-variable calculus, since it(cid:859)s i(cid:374)fi(cid:374)itel(cid:455) easie(cid:396) to appl(cid:455) the te(cid:272)h(cid:374)i(cid:272) of solids of (cid:396)e(cid:448)olutio(cid:374) i(cid:374) si(cid:374)gle (cid:448)a(cid:396)ia(cid:271)le (cid:272)al(cid:272)ulus. I(cid:859)(cid:373) (cid:374)ot su(cid:396)e if i(cid:859)(cid:448)e (cid:272)o(cid:448)e(cid:396)ed e(cid:448)e(cid:396)(cid:455)thi(cid:374)g f(cid:396)o(cid:373) (cid:272)lass, so i(cid:859)ll (cid:271)e so(cid:373)eti(cid:373)es i(cid:374)te(cid:396)p(cid:396)eti(cid:374)g so(cid:373)e thi(cid:374)gs f(cid:396)o(cid:373) the book. Give a 3d object, we take cross sections and it could find formula for the cross sections, then (cid:1874)(cid:1864)(cid:1873)(cid:1865)(cid:1857)= (cid:4666)(cid:1876)(cid:4667)(cid:1856)(cid:1876) (cid:3029) (cid:3028) Note that this (cid:449)e(cid:859)(cid:396)e (cid:374)ot (cid:396)otati(cid:374)g a(cid:396)ou(cid:374)d a(cid:374) a(cid:454)is, fo(cid:396) e(cid:454)a(cid:373)ple: