   Chapter 4.R, Problem 18E

Chapter
Section
Textbook Problem

# Evaluate the integral, if it exists. ∫ 0 2 y 2 1 + y 3   d y

To determine

To evaluate:

02y21+y3dy if it exists

Explanation

1) Concept:

By using the substitution rule for definite integrals and fundamental rule of calculus

2) Theorem and Rule:

Fundamental theorem of calculus:

If f is continuous on [a, b], then abfxdx=Fb-Fa. Substitution rule for definite integrals:

If g' is continuous on [a, b] and f is continuous on the range of u=g(x) then

abfgxg'xdx=g(a)g(b)f(u)du

3) Formula:

xndx=xn+1n+1+C

3) Given:

02y21+y3dy

4) Calculation:

Consider, 02y21+y3dy

Since the function is continuous in the given interval, the integral exists.

By applying substitution rule for definite integrals

Let u=1+y3

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Find more solutions based on key concepts 