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Mathematics
Mathematics
Problem
Match the following
Column I
Column II
(A)
∫
−
1
1
d
x
1
+
x
2
\int_{-1}^{1} \frac{dx}{1+x^2}
∫
−
1
1
1
+
x
2
d
x
(p)
1
2
log
(
2
3
)
\frac{1}{2} \log\left(\frac{2}{3}\right)
2
1
lo
g
(
3
2
)
(B)
∫
0
1
d
x
1
−
x
2
\int_{0}^{1} \frac{dx}{\sqrt{1-x^2}}
∫
0
1
1
−
x
2
d
x
(q)
1
2
log
(
3
2
)
\frac{1}{2} \log\left(\frac{3}{2}\right)
2
1
lo
g
(
2
3
)
(C)
∫
2
3
d
x
1
−
x
2
\int_{2}^{3} \frac{dx}{1-x^2}
∫
2
3
1
−
x
2
d
x
(r)
π
3
\frac{\pi}{3}
3
π
(D)
∫
1
2
d
x
x
x
2
−
1
\int_{1}^{2} \frac{dx}{x\sqrt{x^2-1}}
∫
1
2
x
x
2
−
1
d
x
(s)
π
2
\frac{\pi}{2}
2
π
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