MATH 1007 Lecture Notes - Lecture 17: Farad

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The area a of the region bounded by y=f(x), y=g(x) & the lines x=a and x=b where f and g are coninuous. A = intregral from a to b of [f(x) g(x)]dx. Find the area bounded by y=e^x and bounded below by y=x between x=0 and x=1. Area = integral from 0 to 1 of (e^x x)dx. = e^x x2/2 line from 0 to 1. = [e^1 12/2] [e^0 02/2] = e - 1 + 0. The graph y= -x2 and the lines x=o and x=3. A = integral from 0 to 3 of [0 (-x2)]dx. = integral from 0 to 3 of x^2dx. Ex3: ind the area of the region bounded by y=2x-1 & y=x2-4 and the lines x=1 and x=2. Find the point of intersecion between the curves irst. Set them to equal each other then factor you get intersecions at (3, 5) and (-1, -3)

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