MAT136H1 Lecture Notes - Lecture 8: Late Registration
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MAT136H1 Full Course Notes
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Mat136 lecture 8 finding volumes with integration. Announcements: make sure to enroll in a tutorial. If you have not enrolled in a tutorial, you must complete a late registration form today: you will be starting par2 during your tutorial next week. Last time: we looked at the substitution rule as a technique to evaluate integrals. Today: we apply integration to finding the volumes of 3-dimensional shapes. Let"s (cid:272)o(cid:374)sider (cid:449)hat (cid:449)e did for (cid:1006)-dimensional areas: In 2d shapes, we sliced the area into n number of slices where. Let us now extend this to a 3d shape now: consider the following arbitrary 3d shape: Let"s try a (cid:272)yli(cid:374)der: this is a circular cylinder specifically, we (cid:373)ight also ha(cid:448)e a(cid:374) (cid:862)ar(cid:271)itrary-(cid:271)ased (cid:272)yli(cid:374)der(cid:863, this would work if had a function / expression for the base. Given that a(h) is the area of the cross-section at height h.
