For each of the following integrals find an appropriate trigonometric substitution of the form x = f(t) to simplify the integral. а. (8a sqrt6 sin(theta) dx 8x2+ 2 b. sqrt2 tan(theta) c. 5x2 + 20x+ 13 da dx 18-6x2 -24x d. ||

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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For each of the following integrals find an
appropriate trigonometric substitution of
the form a = f(t) to simplify the integral.
- /(82² – 6)/2 dz
a.
sqrt6 sin(theta)
x2
b.
8x2 +2
x =
sqrt2 tan(theta)
C.
5x2 + 20x + 13 dæ
dx
-18 – 6x2 – 24x
d.
x =
Transcribed Image Text:For each of the following integrals find an appropriate trigonometric substitution of the form a = f(t) to simplify the integral. - /(82² – 6)/2 dz a. sqrt6 sin(theta) x2 b. 8x2 +2 x = sqrt2 tan(theta) C. 5x2 + 20x + 13 dæ dx -18 – 6x2 – 24x d. x =
Evaluate the definite integral.
9 sin()
x3
81 – x2
xp-
0.
[NOTE: Remember to enter all necessary *,
(, and ) !!
Enter arctan (x) for tan-1x, sin(x) for sin x
...]
Transcribed Image Text:Evaluate the definite integral. 9 sin() x3 81 – x2 xp- 0. [NOTE: Remember to enter all necessary *, (, and ) !! Enter arctan (x) for tan-1x, sin(x) for sin x ...]
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