Calculus: 1001 Practice Problems For Dummies (+ Free Online Practice). Patrick Jones
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       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!

       519–522 Find the Riemann sum for the given function with the specified number of intervals using left endpoints.

      519. math, math, math

      520. math, math, math. Round your answer to two decimal places.

      521. math, math, math. Round your answer to two decimal places.

      522. math, math, math. Give your answer in scientific notation, rounded to three decimal places.

       523–526 Find the Riemann sum for the given function with the specified number of intervals using right endpoints.

      523. math, math, math

      524. math, math, math. Round your answer to two decimal places.

      525. math, math, math. Round your answer to two decimal places.

       527–530 Find the Riemann sum for the given function with the specified number of intervals using midpoints.

      527. math, math, math. Round your answer to two decimal places.

      528. math, math, math. Round your answer to two decimal places.

      529. math, math, math. Round your answer to two decimal places.

      530. math, math, math. Round your answer to two decimal places.

       531–535 Find an expression for the definite integral using the definition. Do not evaluate.

      531. math

      532. math

      533. math

      534. math

       536–540 Express the limit as a definite integral. Note that the solution is not necessarily unique.

      536. math

      537. math

      538. math

      539. math

      540. СКАЧАТЬ