Calculus 2 Quiz
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TECHNIQUES OF INTEGRATION
Question 1
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To evaluate the integral
∫
4
6
d
x
x
2
−
8
x
+
25
\int_{4}^{6} \frac{dx}{\sqrt{x^2-8x+25}}
∫
4
6
x
2
−
8
x
+
25
d
x
, which of the following is the most appropriate first step?
A
Substitute
x
=
5
tan
θ
x=5\tan\theta
x
=
5
tan
θ
because the form resembles
x
2
+
a
2
x^2+a^2
x
2
+
a
2
.
B
Complete the square on the quadratic expression in the denominator.
C
Substitute
u
=
x
2
−
8
x
+
25
u=x^2-8x+25
u
=
x
2
−
8
x
+
25
and use the power rule for integration.
D
Substitute
x
=
5
sec
θ
x=5\sec\theta
x
=
5
sec
θ
because of the presence of
x
2
x^2
x
2
and
25
25
25
under the radical.
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