Evaluate the definite integral using the Fundamental Theorem of Calculus. 64 (1 Vx)2 dx 16 2x

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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Evaluate the definite integral using the Fundamental Theorem of Calculus.
64
dx
2x
Transcribed Image Text:Tutorial Exercise Evaluate the definite integral using the Fundamental Theorem of Calculus. 64 dx 2x
Step 1 of 4
Recall The Fundamental Theorem of Calculus.
Let F(x) be any antiderivative of f(x). If f(x) is
Select-
on [a, b], then
f(x) dx =
F(b)
-Select--- v
64
In order to use the Fundamental Theorem of Calculus to evaluate
dx, we must check that
16
2x
the integrand is continuous on the interval [16, 64].
(1 – Vx)?
Since the integrand,
is an algebraic function, it will be continuous everywhere on its domain.
2x
The numerator, (1 Vx), is continuous on the interval
-Select--- v
The denominator, 2x, is equal to zero when x =
(1 - Vx)?
Therefore the domain of f(x) =
-Select--- v
2x
(1-
Thus, f(x) =
-Select--- v continuous on the domain [16, 64].
2x
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Transcribed Image Text:Step 1 of 4 Recall The Fundamental Theorem of Calculus. Let F(x) be any antiderivative of f(x). If f(x) is Select- on [a, b], then f(x) dx = F(b) -Select--- v 64 In order to use the Fundamental Theorem of Calculus to evaluate dx, we must check that 16 2x the integrand is continuous on the interval [16, 64]. (1 – Vx)? Since the integrand, is an algebraic function, it will be continuous everywhere on its domain. 2x The numerator, (1 Vx), is continuous on the interval -Select--- v The denominator, 2x, is equal to zero when x = (1 - Vx)? Therefore the domain of f(x) = -Select--- v 2x (1- Thus, f(x) = -Select--- v continuous on the domain [16, 64]. 2x Submit Skip (you cannot come back)
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