Use geometry (not Riemann sums) to evaluate the definite integral. Sketch the graph of the integrand, show the region in question, and interpret your result. xp X- 6 The integrand is f(x) = /49-x². Graph the integrand. The correct graph is shown below. The area equivalent to the value of the definite integral is the area of the region bounded by the graph, the x-axis, and the lines 2=x pue 0 = X Graph the region in question. The correct graph is shown below. The region is one-fourth of a circle. The area of a circle is equal to xr", where r is the radius of the circle. The radius of the circle L=J S! The area of the region is The net area of the region is 7. Thus, 49-x dx =

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
icon
Related questions
Question
100%

For the parts circled in orange, where did the 4 come from? I pretty much understand the rest was just confused about the 4.

Use geometry (not Riemann sums) to evaluate the definite integral. Sketch the graph of the integrand, show the region in
question, and interpret your result.
49-x2 dx
0.
The integrand is f(x) = / 49 - x2.
%3D
Graph the integrand. The correct graph is shown below.
-12
12
12
The area equivalent to the value of the definite integral is the area of the region bounded by the graph, the x-axis, and the lines
x-0 and x =7.
Graph the region in question. The correct graph is shown below.
-12
12
12
The region is one-fourth of a circle. The area of a circle is equal to ar", where r is the radius of the circle. The radius of the circle
is r=7.
The area of the region is
4.
The net area of the region is
Thus,
= xp
4.
%3D
49-
1/1
https://xlitemprod.pearsoncmg.com/api/v1/print/math
Transcribed Image Text:Use geometry (not Riemann sums) to evaluate the definite integral. Sketch the graph of the integrand, show the region in question, and interpret your result. 49-x2 dx 0. The integrand is f(x) = / 49 - x2. %3D Graph the integrand. The correct graph is shown below. -12 12 12 The area equivalent to the value of the definite integral is the area of the region bounded by the graph, the x-axis, and the lines x-0 and x =7. Graph the region in question. The correct graph is shown below. -12 12 12 The region is one-fourth of a circle. The area of a circle is equal to ar", where r is the radius of the circle. The radius of the circle is r=7. The area of the region is 4. The net area of the region is Thus, = xp 4. %3D 49- 1/1 https://xlitemprod.pearsoncmg.com/api/v1/print/math
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Area of a Circle
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning