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Mathematics
Mathematics
Problem
When
u
=
2
x
+
π
3
u=2x+\dfrac{\pi}{3}
u
=
2
x
+
3
π
is substituted in
∫
0
π
cos
(
2
x
+
π
3
)
d
x
\displaystyle \int_{0}^{\pi}\!\cos(2x+\tfrac{\pi}{3})\,dx
∫
0
π
cos
(
2
x
+
3
π
)
d
x
, which of the following gives the correct new limits of integration
(
u
lower
,
u
upper
)
(u_\text{lower},u_\text{upper})
(
u
lower
,
u
upper
)
? a)
(
π
3
,
5
π
3
)
\bigl(\dfrac{\pi}{3},\,\dfrac{5\pi}{3}\bigr)
(
3
π
,
3
5
π
)
b)
(
0
,
2
π
)
(0,2\pi)
(
0
,
2
π
)
c)
(
π
3
,
7
π
3
)
\bigl(\dfrac{\pi}{3},\,\dfrac{7\pi}{3}\bigr)
(
3
π
,
3
7
π
)
d)
(
π
3
,
4
π
3
)
\bigl(\dfrac{\pi}{3},\,\dfrac{4\pi}{3}\bigr)
(
3
π
,
3
4
π
)
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