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Mathematics
Mathematics
Problem
Evaluate
∫
d
x
a
2
−
x
2
\displaystyle \int \frac{dx}{\sqrt{a^{2}-x^{2}}}
∫
a
2
−
x
2
d
x
, where
a
>
0
a>0
a
>
0
. a)
1
a
tan
−
1
x
a
+
C
\dfrac{1}{a}\tan^{-1}\dfrac{x}{a}+C
a
1
tan
−
1
a
x
+
C
b)
cos
−
1
x
a
+
C
\cos^{-1}\dfrac{x}{a}+C
cos
−
1
a
x
+
C
c)
sin
−
1
x
a
+
C
\sin^{-1}\dfrac{x}{a}+C
sin
−
1
a
x
+
C
d)
1
a
sin
−
1
x
a
+
C
\dfrac{1}{a}\sin^{-1}\dfrac{x}{a}+C
a
1
sin
−
1
a
x
+
C
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