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CBSE
MATHEMATICS · Multi correct · CBSE · Mathematics · Integrals · Integrals
Problem
If
∫
sin
−
1
x
cos
−
1
x
d
x
=
f
−
1
(
x
)
[
A
x
−
x
f
−
1
(
x
)
−
2
1
−
x
2
]
+
π
2
1
−
x
2
+
2
x
+
C
\int \sin^{-1}x\cos^{-1}x\,dx=f^{-1}(x)\left[Ax-xf^{-1}(x)-2\sqrt{1-x^2}\right]+\frac{\pi}{2}\sqrt{1-x^2}+2x+C
∫
sin
−
1
x
cos
−
1
x
d
x
=
f
−
1
(
x
)
[
A
x
−
x
f
−
1
(
x
)
−
2
1
−
x
2
]
+
2
π
1
−
x
2
+
2
x
+
C
, then (a)
f
(
x
)
=
sin
x
f(x)=\sin x
f
(
x
)
=
sin
x
(b)
f
(
x
)
=
cos
x
f(x)=\cos x
f
(
x
)
=
cos
x
(c)
A
=
π
4
A=\frac{\pi}{4}
A
=
4
π
(d)
A
=
π
2
A=\frac{\pi}{2}
A
=
2
π
Related theory
Advanced Differentiation
Integration by Parts
Integration Techniques
Integrals
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