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Mathematics
Mathematics
Problem
Which of the following definite integral(s) vanishes? a.
∫
0
π
/
2
ln
(
cot
x
)
d
x
\int_{0}^{\pi/2} \ln(\cot x) dx
∫
0
π
/2
ln
(
cot
x
)
d
x
b.
∫
0
2
π
sin
3
x
d
x
\int_{0}^{2\pi} \sin^3 x dx
∫
0
2
π
sin
3
x
d
x
c.
∫
1
/
e
e
d
x
x
(
ln
x
)
1
/
3
\int_{1/e}^{e} \frac{dx}{x(\ln x)^{1/3}}
∫
1/
e
e
x
(
l
n
x
)
1/3
d
x
d.
∫
0
π
1
+
cos
2
x
2
d
x
\int_{0}^{\pi} \sqrt{\frac{1 + \cos 2x}{2}} dx
∫
0
π
2
1
+
c
o
s
2
x
d
x
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