   Chapter 4.4, Problem 44E

Chapter
Section
Textbook Problem

# Use a graph to estimate the x-intercepts of the curve y = 1 − 2 x − 5 x 4 . Then use this information to estimate the area of the region that lies under the curve and above the x-axis.Repeat Exercise 43 for the curve y = 2 x + 3 x 4 − 2 x 6 .

To determine

To estimate:

The x-intercepts and using the intercepts, find the area of the region that lies under the curve and above the  x  axis.

Explanation

1) Concept:

The fundamental theorem of calculus part 2: If  f  is continuous on a,b, then abfxdx=Fb-Fa,  where  F  is any antiderivative of f , that is, the function  F  such that F'=f .

2) Formula:

fx+gxdx=fxdx+gxdx

xndx=xn+1n+1+C

kdx=kx+C

3) Given:

y=2x+3x4-2x6

4) Calculation:

Consider the given curve,

y=2x+3x4-2x6

The graph of the given curve is

By using the graph of given curve, the x  intercept of the given curve is x0, x1.38

Next, find the area of the region that lies under the curve and above the  x  axis.

From the graph, the curve  y=2x+3x4-2x6 bounded between x=0  and  x=1.38  is continuous on 0, 1.38 and then, the area of the region that lies under the curve and above the x  axis is

01.38(2x+3x4-2x6)dx

To find area of region lies under the curve and above the x  axis, evaluate the definite integral

### 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

#### Evaluate the expression sin Exercises 116. 3(2)0

Finite Mathematics and Applied Calculus (MindTap Course List)

#### If f(x) = (x a)(x b)(x c), show that f(x)f(x)=1xa+1xb+1xc

Single Variable Calculus: Early Transcendentals, Volume I

#### For y=43+2x, y = _____. a) 4(3 + 2x)3/2 b) 4(3 + 2x)3/2 c) 2(3 + 2x)1/2 d) 2(3 + 2x)1/2

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 