Estimating the area under a curve typically involves quite a bit of arithmetic but shouldn’t be too difficult conceptually. The process should be straightforward after you do a few problems.
The problems on expressing a given Riemann sum as a definite integral don’t always have unique solutions.
To evaluate the problems involving Riemann sums, you need to know a few summation formulas. You can find them in any standard calculus text if you don’t remember them — or you can derive them!
Calculating Riemann Sums Using Left Endpoints
519–522 Find the Riemann sum for the given function with the specified number of intervals using left endpoints.
519.
520.
521.
522.
Calculating Riemann Sums Using Right Endpoints
523–526 Find the Riemann sum for the given function with the specified number of intervals using right endpoints.
523.
524.
525.
526.
Calculating Riemann Sums Using Midpoints
527–530 Find the Riemann sum for the given function with the specified number of intervals using midpoints.
527.
528.
529.
530.
Using Limits and Riemann Sums to Find Expressions for Definite Integrals
531–535 Find an expression for the definite integral using the definition. Do not evaluate.
531.
532.
533.
534.
535.
Finding a Definite Integral from the Limit and Riemann Sum Form
536–540 Express the limit as a definite integral. Note that the solution is not necessarily unique.
536.
537.
538.
539.
540.
