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Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.4: Values Of The Trigonometric Functions

Problem 22E

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Question

Integrals Resulting in Inverse Trigonometric Functions.
The table below contains the derivatives of the inverse trigonometric functions that arise frequently in integration.
d
sin
dx
(a" (금))
1
d
(cos" ())
-1
-1
-1
|x| < a
|리 < a
dx
Va2
("() -
d
1
d
-1
-1
tan
cot
da
a2 + x²
da
a2 + x2
a
E)
d
1
d
-1
-1
sec
|æ|> a
dx
-1
csc
|x| >
dx
a
a2
a
ryx2 - g2
With help from the table above, evaluate the following indefinite integral. Hint: a simple substitution may help.
7 sec (4)
dt
tyt4 – 49
-1
Note: answer should be in terms of t only.

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