# Definite Integral as the Limit of a sum

Calculus

Integral Calculus(II)

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(part 2).

Find by the method of summation the value of:

(a) ∫ x^3dx, where the lower limit is 0 and the upper limit is 1,

i.e., integral of x^3, where the lower limit is 0 and the upper limit is 1.

(b) ∫ (ax + b)dx, where the lower limit is 0 and the upper limit is 1,

i.e., integral of (ax + b), where the lower limit is 0 and the upper limit is 1.

See the attached file.

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#### Solution Preview

Calculus

Integral Calculus(II)

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:

Find by the method of summation the value of:

(a) ∫ x^3dx, where the lower limit is 0 and the upper limit is 1,

i.e., integral of x^3, where the lower limit is 0 and the upper limit is 1.

(b) ∫ (ax + b)dx, where the lower limit is 0 and the upper limit is 1,

i.e., integral of (ax + b), where the lower limit is 0 and the upper limit is 1.

Solution contains detailed step-by-step explanation.