Question:

Evaluate s dx , for x>4, in two ways: using partial fractions and a trigonometric substitution. Reconcile your two 2 x - 16 answ

Evaluate
s
dx
, for x>4, in two ways: using partial fractions and a trigonometric substitution. Reconcile your two
2
x - 16
answers.
First evaluate
S
dx
x? - 16
using partial fractions. Factor the denominator of the integrand.
x2 - 16 = (x+4)(x-4)
Using the result of the previous step, rewrite the integrand using partial fraction decomposition.
dx
A
B
+
dx
X-4
|x+4|
x - 16
Solve for A and B.
1
A= and B=
8
8
(Type integers or simplified fractions.)
Substitute the determined values for A and B into the integrand from a previous step and integrate.
dx
X-4
s
1
In
8
+ C
X? - 16
X+4

Evaluate s dx , for x>4, in two ways: using partial fractions and a trigonometric substitution. Reconcile your two 2 x - 16 answers. First evaluate S dx x? - 16 using partial fractions. Factor the denominator of the integrand. x2 - 16 = (x+4)(x-4) Using the result of the previous step, rewrite the integrand using partial fraction decomposition. dx A B + dx X-4 |x+4| x - 16 Solve for A and B. 1 A= and B= 8 8 (Type integers or simplified fractions.) Substitute the determined values for A and B into the integrand from a previous step and integrate. dx X-4 s 1 In 8 + C X? - 16 X+4

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