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Midpoint and Trapezoidal Rules
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Approximating Integrals
There are some cases when it is impossible to find the definite integral They can be approximated by using types of Riemann sums animations
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Midpoint Rule Midpoints of drawn rectangles are used where
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Trapezoidal Rule Uses trapezoids instead of rectangles
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Example Use both the Midpoint and Trapezoidal rules to evaluate the integral with n = 5
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Practice Use both the midpoint and trapezoidal rule to find the integral below for n = 4
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Simpson’s Rule Simpson’s Rule uses parabolas rather than rectangles to approximate the integral Numerical Analysis Animations
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Example Use Simpson’s Rule to find the integral below for n = 10
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