Use the Midpoint Rule with n = 4 to estimate the work W done by the force in moving an object from x = 5 to x = 37.The table shows values of a force function f(x), where x is measured in meters and...

Use the Midpoint Rule with n = 4 to estimate the work W done by the force in moving an object from x = 5 to x = 37.

The table shows values of a force function f(x), where x is measured in meters and f(x) in newtons. Use the Midpoint Rule with n = 4 to estimate the work W done by the force in moving an object from x = 5 to x = 37.

x 5 9 13 17 21 25 29 33 37 f(x) 5 5.5 6.8 8.8 9.8 8.1 6.7 5.4 4.2

 

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embizze | High School Teacher | (Level 1) Educator Emeritus

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Given x| 5   9   13   17   21   25   29   33   37
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      f(x)| 5 5.5 6.8  8.8  9.8  8.1  6.7  5.4  4.2

If n=4, the width of the intervals is `Delta=(37-5)/4=8`

We can estimate `int_5^(37)f(x)dx` by `sum_(i=1)^4f(m_i)Delta` where `m_i` is the midpoint of the `i^(th)` interval.

Thus `sum_(i=1)^4f(m_i)Delta=8[5.5+8.8+8.1+5.4]=222.4`

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The amount of work done is approximately 222.4J

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