# Definite Integral as the Limit of a sum

Calculus

Integral Calculus(IX)

Definite Integral as the Limit of a sum

Method of Summation

Definite Integral

It is an explanation for finding the integral by the method of summation i.e., by evaluating

the integral as limit of a sum(part 9).

Evaluate the definite integral

∫ sin nxdx, where the lower limit is 0 and the upper limit is a,

i.e., integral of sin nx, where the lower limit is 0 and the upper limit is a.

as limit of a sum.

See the attached file.

Â© BrainMass Inc. brainmass.com May 24, 2023, 2:01 pm ad1c9bdddfhttps://brainmass.com/math/integrals/definite-integral-as-the-limit-of-a-sum-42264

#### Solution Preview

Calculus

Integral Calculus(IX)

Definite Integral as the Limit of a sum

Method of Summation

...

#### Solution Summary

This solution is comprised of a detailed explanation for finding the value of the definite integral by

using the method of summation.

It contains step-by-step explanation for the following problem:

Evaluate the definite integral

∫ sin nxdx, where the lower limit is 0 and the upper limit is a,

i.e., integral of sin nx, where the lower limit is 0 and the upper limit is a

as limit of a sum.

Solution contains detailed step-by-step explanation.