Calculus 1 Quiz
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INTEGRATION: ACCUMULATION & FTC
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Which substitution would be most effective for evaluating the integral
∫
d
x
x
2
x
2
−
9
\int \frac{dx}{x^2\sqrt{x^2-9}}
∫
x
2
x
2
−
9
d
x
?
A
A u-substitution,
u
=
x
2
−
9
u = x^2-9
u
=
x
2
−
9
, to simplify the term inside the radical.
B
A trigonometric substitution,
x
=
3
sin
(
θ
)
x = 3 \sin(\theta)
x
=
3
sin
(
θ
)
, based on the form
a
2
−
x
2
\sqrt{a^2-x^2}
a
2
−
x
2
.
C
A trigonometric substitution,
x
=
3
sec
(
θ
)
x = 3 \sec(\theta)
x
=
3
sec
(
θ
)
, based on the form
x
2
−
a
2
\sqrt{x^2-a^2}
x
2
−
a
2
.
D
A trigonometric substitution,
x
=
3
tan
(
θ
)
x = 3 \tan(\theta)
x
=
3
tan
(
θ
)
, based on the form
x
2
+
a
2
\sqrt{x^2+a^2}
x
2
+
a
2
.
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