Q. 15 - Calculus

Question

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

$\pi {\int }_0^2{x}^{4}dx and \pi {\int }_0^2(x^4-16)dx$

Step-by-Step Solution

Answer

The integral $\pi {\int }_0^2{x}^{4}dx$ is bigger

Step 1: Given information

We are given two integrals

$\pi {\int }_0^2{x}^{4}dx and \pi {\int }_0^2(x^4-16)dx$

Step 2: Explaination

The term $x^4 is bigger than term x^4-16$

Hence on integrating we will get the term 16x in second integral And after substituting the limits the second term will be 16 less than that of first term. Hence the first term is bigger