Trapezoidal sum approximation

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Trapezoid Approximation Slide 41 / 175 Return to Table of Contents Trapezoid Approximation [This object is a pull tab] Teacher Notes up the idea of using different shapes Students may have already brought to approximate area; if not, you can bring it up now and ask for ideas to gain a closer approximation rather than using rectangles.

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Answer to Find the trapezoidal Riemann sum approximation of fo Vx2 + 3dx using four equal partitions. KO) + (4) + (0.5)[A1) + 2) +...

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Use the trapezoidal sum commands to calculate ten-decimal-place approximations to the area under the curve f (x) = 1/x above the interval [1,3] on the x-axis. Do approximations for n = 5 subintervals, for n = 10 subintervals, for n = 20 subintervals, and for n = 40 subintervals. Trapezoidal and Midpoint Approximations. Definite integral computed as the sum of the area of trapezoidal segments.

In the command below, the number of subintervals is set to 10, but you should experiment with increasing or decreasing this number. Note that Maple writes out the sum and doesn't evaluate it to a number. >trapezoid(f(x),x=0..2,10); Putting an evalf command on the outside computes the trapezoidal approximation. >evalf(trapezoid(f(x),x=0..2,10)); Use the trapezoidal sum commands to calculate ten-decimal-place approximations to the area under the curve f (x) = 1/x above the interval [1,3] on the x-axis. Do approximations for n = 5 subintervals, for n = 10 subintervals, for n = 20 subintervals, and for n = 40 subintervals. We can approximate a definite integral, $\int_a^b f(x)dx$, using a variety of Riemann sums. As you observed, the midpoint method is typically more accurate than the trapezoidal method.