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Mathematics
Mathematics
Problem
Find the value of the integral
∫
d
x
9
−
6
x
−
x
2
\displaystyle\int \frac{dx}{\sqrt{9-6x-x^{2}}}
∫
9
−
6
x
−
x
2
d
x
. a. (i) Rewrite the quadratic expression
9
−
6
x
−
x
2
9-6x-x^{2}
9
−
6
x
−
x
2
so that the radicand is expressed in the form
a
2
−
(
x
−
h
)
2
a^{2}-(x-h)^{2}
a
2
−
(
x
−
h
)
2
, where
a
a
a
and
h
h
h
are constants. b. (ii) Hence, evaluate
∫
d
x
9
−
6
x
−
x
2
\displaystyle\int \frac{dx}{\sqrt{9-6x-x^{2}}}
∫
9
−
6
x
−
x
2
d
x
.
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