Steven N.

asked • 10/02/23

Trapezodial, midpoint, and Simpsons rule

Here is a problem I can't help my daughter with. Any help is appreciated.


Use the trapezoidal rule, the midpoint rule, and Simpson's rule to approximate the integral 1 to 7 (ln(x)/4+x)dx

Steven N.

She was able to get t8 and s8, just not m8
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10/02/23

Doug C.

I have a feeling this is intended as [ln(x)/(4+x)] ??
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10/02/23

Doug C.

Also you mention t8 and s8, but the original post does not suggest n = 8?
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10/02/23

Bradford T.

Midpoint rule: Δx(f((x0​+x1​​)/2)+f((x1​+x2​​)/2)+f((x2​+x3​​)/2)+⋯+f((xn−2​+xn−1​​)/2)+f((xn−1​+xn)/2​​)), where Δx=(b-a)/n
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10/02/23

Doug C.

Here is a graph to help check your work: desmos.com/calculator/wk4etycon7
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10/02/23

1 Expert Answer

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Doug C. answered • 10/03/23

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desmos.com/calculator/jgonfrkmyh


The above graph allows you to calculate Riemann sum for left-hand, right-hand, and midpoint.


Here is a graph showing the trapezoidal rule.


desmos.com/calculator/2ka7wkzbmz



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