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Question 57
Mu
Improper Integrals
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Question
If
a
+
b
=
2
a+b=2
a
+
b
=
2
,
a
>
b
>
0
a>b>0
a
>
b
>
0
, evaluate
∫
1
/
2
1
d
x
x
a
(
1
−
x
)
b
\displaystyle\int_{1/2}^1\frac{dx}{x^a(1-x)^b}
∫
1/2
1
x
a
(
1
−
x
)
b
d
x
.
A.
b
+
2
a
−
1
\frac{b+2}{a-1}
a
−
1
b
+
2
B.
b
+
1
a
−
1
\frac{b+1}{a-1}
a
−
1
b
+
1
C.
2
a
\frac2a
a
2
D.
1
a
−
1
\frac1{a-1}
a
−
1
1
E.
NOTA
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