MATH 1272 Lecture Notes - Lecture 1: If And Only If
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Assumptions made f,g both integrable on [a,b] f,g both continuous on [a,b] f(x) 0, g(x) 0 on [a,b] f(x) g(x) on [a,b] Method 1- split up every time the graphs cross. Partition [a,b] into n pieces of width x=(b-a)/n. To have a unified formula without knowing which function is bigger, Note! if f(x) g(x) on [a,b], we can drop absolute values. Find the area of the region shown below. Rewrote without absolute value by looking at the graph to see when sin(x) Use integrals to express the area of the region bounded on the left by y =2x+7 and on the right by y=x. To find b,c, solve (i. e. , find points of intersection) To find a, solve 0 =2x+7 for x (i. e. , find x intercept) Make sure bounds go from smaller to larger. If you don"t rotate, integrand is right curve-left curve.
