Lecture12bc

# Lecture12bc - function. Therefore, the left-most region...

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Instructor: Quanlei Fang Dept. of Math, University at Buffalo, Spring 2009 Welcome to Math 122 Lecture 12 Survey of Calculus and its Applications I1 § 9.3 (Contd) Evaluation of Definite Integrals ! The Definite Integral ! Evaluating Definite Integrals ! Change of Limits Rule

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Find the area of the shaded region. To find the area of the shaded region, we will integrate the given function. But we must know what our limits of integration will be. Therefore, we must determine the three x -intercepts of the function. This is the given

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Unformatted text preview: function. Therefore, the left-most region (above the x-axis) starts at x = -3 and ends at x = 0. The right-most region (below the x-axis) starts at x = 0 and ends at x = 3. So, to find the area in the shaded regions, we will use the following. Replace y with 0 to find the x-intercepts. Set each factor equal to 0. Solve for x . Now let’s find an antiderivative for both integrals. Evaluate. ln x 1 e " dx Evaluate. xe " x ln2 # dx Evaluate the definite integral x ( x + 1) 2 + 2ln x x 1 2 " dx...
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## This note was uploaded on 02/20/2009 for the course MTH 122 taught by Professor Buettgens during the Spring '08 term at SUNY Buffalo.

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Lecture12bc - function. Therefore, the left-most region...

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