Write an equation to relate the given and the to find. Reduce the number of variables to 2. Find the derivative and Critical Numbers. Test the critical numbers for max or min, using 1st derivative or 2nd derivative test, and state solution. Is "to find" found? Does solution make sense? Using the Limit Definition to Find Area: Sketch the function f and indicate the region on the interval [a,b].
Is f continuous and nonnegative on the interval? Substitute c i for x in the function and proceed with the sums, using Summation Formulas, Theorum 4. Evaluate the limits at infinity. Find the points of intersection of the curves. If the curves are close and orientation is difficult to determine, substitute values between those of the points of intersection to determine which is above or to the right of the other.
Use the sketch to determine which integral to use: If each curve passes the vertical line test in the bounded region, use vertical rectangles, the x variable, and the integral: If a curve fails the vertical line test but passes the horizontal line test in the bounded region, use horizontal rectangles, the variable y, and the integral: If the bounded area contains more than one distinct region, write the area as the sum of the areas of each distinct region. Get a real tutor anytime, anywhere in our online classroom.
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