MATH138 Midterm: MATH138, lec 5 term test 1
15 Sep 2018
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Say we want to find the area between () and () from = to = f x g x b a. Example: find the area between () =2 and () = from = 1 to = 3. Area between () and () from = to = is. The upper curve may change over the interval. So let us write down the official formula. Example: find the area between () = sin and () = cos from = 0 to = Example: find the area enclosed by () = 2 2 and () =2. We can find the volume of certain objects (areas with enough symmetry) Idea: divide the region u into infinitely many infinitely thin pieces, each with area () (for each ) Then volume is equal to ( )a x f x a b dx. Find the volume of shapes with radius . 2 x r r () =()2 = 2 2 2 =(2 2)
