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

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
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