Consider the following function. 25 - dx x2 (a) Determine an appropriate trigonometric substitution. O Use x = tan(0), where - < 0 < since the integrand contains the expression V 25 – x². Use x = 25sec(0), where 0 s0 < or n < 0 < 2 since the integrand contains the expression V 25 – x 2 O Use x = 25sin(0), where since the integrand contains the expression 2 25 - x2. O Use x = 5sin(0), where - since the integrand contains the expression - x2. 2 25 - Зл since the integrand contains the expression 2 O Use x = 5sec(0), where 0 s0 < ~ or a s0 < 2 25 - O Use x = 5tan(0), where - < 0 < since the integrand contains the expression 2 - x2. 25 - (b) Apply the substitution to transform the integral into a trigonometric integral. Do not evaluate the integral. x4 dx = de 25 - x2

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...
Question
Consider the following function.
dx
25 - x2
(a) Determine an appropriate trigonometric substitution.
Use x = tan(0), where -
< 0 <
2
since the integrand contains the expression V 25 – x².
2
-
-
O Use x = 25sec(0), where 0 < 0 <
or n < 0 <
2
since the integrand contains the expression V 25 – x².
2
Use x = 25sin(0), where
since the integrand contains the expression V 25 – x².
2
Use x = 5sin(0), where -
, since the integrand contains the expression V 25 –
2
|
2
– x².
Use x =
5sec(0), where 0 < 0 <
or I < 0 <
2
since the integrand contains the expression V 25 –
2
1-
-x².
Use x = 5tan(0), where -
IT
since the integrand contains the expression V 25 -
-x².
(b) Apply the substitution to transform the integral into a trigonometric integral. Do not evaluate the integral.
+8
25 - x2
= xp
de
V
Transcribed Image Text:Consider the following function. dx 25 - x2 (a) Determine an appropriate trigonometric substitution. Use x = tan(0), where - < 0 < 2 since the integrand contains the expression V 25 – x². 2 - - O Use x = 25sec(0), where 0 < 0 < or n < 0 < 2 since the integrand contains the expression V 25 – x². 2 Use x = 25sin(0), where since the integrand contains the expression V 25 – x². 2 Use x = 5sin(0), where - , since the integrand contains the expression V 25 – 2 | 2 – x². Use x = 5sec(0), where 0 < 0 < or I < 0 < 2 since the integrand contains the expression V 25 – 2 1- -x². Use x = 5tan(0), where - IT since the integrand contains the expression V 25 - -x². (b) Apply the substitution to transform the integral into a trigonometric integral. Do not evaluate the integral. +8 25 - x2 = xp de V
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