Q. 16 - Calculus

Question

For each pair of definite integrals in exercise 13-18 decide which if either is larger without computing the integrals 

$\pi {\int }_0^3{x}^{2}dx and \pi {\int }_0^3(9-x^2)dx$

Step-by-Step Solution

Answer

The integral $\pi {\int }_0^3(9-x^2)dx$ is bigger

Step 1: Given information

We are given two integrals

$\pi {\int }_0^3{x}^{2}dx and \pi {\int }_0^3(9-x^2)dx$

Step 2 : Explaination

The term $x^2 is bigger 9-x^2 on integrating$

And after substituting the limits in the integrated value the second term will be 9 more than that of the first term.

Hence the second term is bigger