1

Problem

Evaluate \$ \int (x^2) dx\$ with limits from 1 to 3.

2

Step

The power rule

\$\int x^n = x^(n + 1)/(n + 1) + C \$

3

Step

We can use the power rule after simplification to find the antiderivative of \$x^2\$.

\$ \int (x^2) dx = x^(2 + 1)/(2 + 1) + C\$

\$ \int (x^2) dx = (x^3)/3 + C\$

4

Step

To evaluate the definite integral from 1 to 3, we substitute limits, apply antiderivative, and find the difference.

\$ 1/3(x^3)_1^3 = 1/3 (3^3 - 1^3)\$

\$ 1/3(x^3)_1^3 = 1/3 (27 - 1)\$

5

Step

After simplification

\$ 1/3(x^3)_1^3 = 1/3 (26)\$

\$ 1/3(x^3)_1^3 = (26)/3 \$

6

Solution

The limits from 1 to 3 is \$ 1/3(x^3)_1^3 = (26)/3 \$.

7

Sumup

Please summarize Problem, Clue, Hint, Formula, Steps and Solution

Choices

8

Choice-A

This statement is inaccurate due to an error in the value, it needs correction from \$(23)/3\$ to \$(26)/3\$ for accuracy

Wrong \$(23)/3\$

9

Choice-B

This statement is inaccurate due to an error in the value, it needs correction from \$(28)/3\$ to \$(26)/3\$ for accuracy

Wrong \$(28)/3\$

10

Choice-C

When you plug in the specified values, the definite integral yields a result of \$(26)/3\$

Correct \$(26)/3\$

11

Choice-D

This statement is inaccurate due to an error in the value, it needs correction from \$(35)/3\$ to \$(26)/3\$ for accuracy

Wrong \$(35)/3\$

12

Answer

Option

C

13

Sumup

Please summarize choices