Visual proof Let F(x) = S¿ Vď – ² đt. The figure shows that F(x) = area of sector OAB + area of triangle OBC. %3D a. Use the figure to prove that a sin'(x/a) , xVa – x² F(x) = b. Conclude that a² sin-"(x/a) xVa – x? + C. 2 (Source: The College Mathematics Journal, 34, 3, May 2003) y. A a y = Va? - B

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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Visual proof Let F(x) = S¿ Vď – ² đt. The figure shows that
F(x) = area of sector OAB + area of triangle OBC.
%3D
a. Use the figure to prove that
a sin'(x/a) , xVa – x²
F(x) =
b. Conclude that
a² sin-"(x/a) xVa – x?
+ C.
2
(Source: The College Mathematics Journal, 34, 3, May 2003)
y.
A
a
y = Va? -
B
Transcribed Image Text:Visual proof Let F(x) = S¿ Vď – ² đt. The figure shows that F(x) = area of sector OAB + area of triangle OBC. %3D a. Use the figure to prove that a sin'(x/a) , xVa – x² F(x) = b. Conclude that a² sin-"(x/a) xVa – x? + C. 2 (Source: The College Mathematics Journal, 34, 3, May 2003) y. A a y = Va? - B
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