Solution Found!
Comparing areas On the interval [0, 2], the graphs of f(x)
Chapter 4, Problem 62E(choose chapter or problem)
Comparing areas On the interval [0,2], the graphs of \(f(x)=x^{2} / 3\) and \(g(x)=x^{2}\left(9-x^{2}\right)^{-1 / 2}\) have similar shapes.
(a) Find the area of the region bounded by the graph of f and the x-axis on the interval [0,2].
(b) Find the area of the region bounded by the graph of g and the x-axis on the interval [0,2].
(c) Which region has the greater area?
Questions & Answers
QUESTION:
Comparing areas On the interval [0,2], the graphs of \(f(x)=x^{2} / 3\) and \(g(x)=x^{2}\left(9-x^{2}\right)^{-1 / 2}\) have similar shapes.
(a) Find the area of the region bounded by the graph of f and the x-axis on the interval [0,2].
(b) Find the area of the region bounded by the graph of g and the x-axis on the interval [0,2].
(c) Which region has the greater area?
ANSWER:Problem 62E
Solution:-
Step1
Given that
Areas On the interval [0, 2], the graphs of f(x) = x2/3 and g(x) = x2(9 – x2)–1/2 have similar shapes.
Step2
To find
a. Find the area of the region bounded by the graph of f and the x-axis on the interval [0, 2].
b. Find the area of the region bounded by the graph of g and the x-axis on the interval [0, 2].
c. Which region has the greater area?
Step3
a.The area of the region bounded by the graph of f and the x-axis on the interval [0, 2]
f(x)=
Area=
=
=
=
=
=+C
Step4
Put values to find area
Area==
Therefore, The area of the region bounded by the graph of