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Bangladesh Contests
Bangladesh Mathematical Olympiad
2018 Bangladesh Mathematical Olympiad
7
7
Part of
2018 Bangladesh Mathematical Olympiad
Problems
(1)
Evaluate the value of the trignometric function
Source: Bangladesh National Mathematical Olympiad 2018
2/23/2019
Evaluate
∫
0
π
/
2
cos
4
x
+
sin
x
cos
3
x
+
sin
2
x
cos
2
x
+
sin
3
x
cos
x
sin
4
x
+
cos
4
x
+
2
s
i
n
x
cos
3
x
+
2
sin
2
x
cos
2
x
+
2
sin
3
x
cos
x
d
x
\int^{\pi/2}_0 \frac{\cos^4x + \sin x \cos^3 x + \sin^2x\cos^2x + \sin^3x\cos x}{\sin^4x + \cos^4x + 2\ sinx\cos^3x + 2\sin^2x\cos^2x + 2\sin^3x\cos x} dx
∫
0
π
/2
s
i
n
4
x
+
c
o
s
4
x
+
2
s
in
x
c
o
s
3
x
+
2
s
i
n
2
x
c
o
s
2
x
+
2
s
i
n
3
x
c
o
s
x
c
o
s
4
x
+
s
i
n
x
c
o
s
3
x
+
s
i
n
2
x
c
o
s
2
x
+
s
i
n
3
x
c
o
s
x
d
x
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geometry
trigonometry
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