Use the substitution x = 2 sint, - ≤t≤ to simplify the following integral: 플 1 4 - x2 dx (a) Calculate √√4x² in terms of t. (b) If the substitution replaces dx with f(t) dt then what is the function f(t)? f(t) = S (d) Perform this integral, including constant of integration c. (c) Hence write the integral in terms of t: (e) Convert your answer from a function of t to a function of x. To dt.

Calculus: Early Transcendentals
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ISBN:9781285741550
Author:James Stewart
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Chapter1: Functions And Models
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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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Hi, I would like to have the solutions to the questions below. Can you write down detailed explanation for me, please?

Use the substitution x = 2 sint,
4
1
x²
dx
(a) Calculate 4 - 24
x2 in terms of t.
≤t≤ to simplify the following integral:
(b) If the substitution replaces dx with f(t) dt then what is the function f(t)?
f(t) =
(c) Hence write the integral in terms of t:
,
(d) Perform this integral, including constant of integration c.
(e) Convert your answer from a function of t to a function of x.
QI
dt.
Transcribed Image Text:Use the substitution x = 2 sint, 4 1 x² dx (a) Calculate 4 - 24 x2 in terms of t. ≤t≤ to simplify the following integral: (b) If the substitution replaces dx with f(t) dt then what is the function f(t)? f(t) = (c) Hence write the integral in terms of t: , (d) Perform this integral, including constant of integration c. (e) Convert your answer from a function of t to a function of x. QI dt.
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