Math $251$ SLO$2$

Student Name:

$q,$

Instructor Name: $q,$

This assignment will lead you through approximating ${\displaystyle \underset{0}{\overset{\frac{}{2}}{}}}cosxdx$ using a Riemann sum with $6$ midpoint rectangles. Calculator instructions for simplifying this process are given on the next page.

Find the width of each rectangle by hand. Record your result in the space provided.

Round your answer correct to $3$ decimal places.

$\frac{\frac{}{2}-0}{6}=\frac{}{12}=0\mathrm{.}262$

Find all six midpoints and record your answers in the table below.

Round your answers correct to $3$ decimal places.

$\frac{x_k+x_{k+1}}{2}$

Find the heights of all six rectangles and record your answers in the table below.

Round your answers correct to $3$ decimal places.

$\backslash$table$[[$Rectangle$,$Midpoint,Height$],[1,,],[2,,],[3,,],[4,,],[5,,],[6,,]]$

Write out the entire Riemann sum using the values from the table above.

Keep all values rounded correct to $3$ decimal places.

$5.$ Evaluate the Riemann sum.

Round your answer correct to $3$ decimal places.

$6.$ Evaluate the following integral.

${\displaystyle \underset{0}{\overset{\frac{}{2}}{}}}cosxdx=$

Was the Riemann sum an overestimate or underestimate to the exact value?