   Chapter 4.5, Problem 63E

Chapter
Section
Textbook Problem

Evaluating a Definite Integral In Exercises 61-68, evaluate the definite integral. Use a graphing utility to verify your result. ∫ 1 2 2 x 2 x 3 + 1   d x

To determine

To calculate: The definite integral 122x2x3+1dx and also verify it by using Ti-83.

Explanation

Given:

The provided integral is:

122x2x3+1dx

Formula used:

According to theorem for change of variable for indefinite integrals;

If u=g(x) then du=g'(x)

Then integral will take the following form,

f(g(x))g'(x)dx=f(u)du=F(u)+C

As according to fundamental theorem of calculus,

abf(x)dx=F(b)F(a)

Calculation:

Consider, u=x3+1

Also, when

x=1x3=1x3+1=1+1u=2

And,

x=2x3=8x3+1=8+1u=9

Then on differentiating above equation with respect to x we get,

dudx=3x2+0du3=x2dx

Multiplying both side by 2,

(2)du3=2x2dx

Convert the integral in terms of u

122x2

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

In Exercises 4756, solve the given equation for the indicated variable. 4=2x

Finite Mathematics and Applied Calculus (MindTap Course List)

If f(x) = 5x, show that f(x+h)f(x)h=5x(5h1h)

Single Variable Calculus: Early Transcendentals, Volume I

In Exercises 39-54, simplify the expression. (Assume that x, y, r, s, and t are positive.) 40. (49x2)1/2

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

In problems 23-58, perform the indicated operations and simplify. 27.

Mathematical Applications for the Management, Life, and Social Sciences

Find the distance between the points. 2. (1, 3), (5, 7)

Single Variable Calculus: Early Transcendentals 