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Mathematics
Mathematics
Problem
Evaluate the following integrals and use the results to compute a definite integral. (i) Find
∫
sin
(
5
x
−
2
)
d
x
\displaystyle \int \sin(5x-2)\,dx
∫
sin
(
5
x
−
2
)
d
x
. (ii) Find
∫
e
7
x
+
1
d
x
\displaystyle \int e^{7x+1}\,dx
∫
e
7
x
+
1
d
x
. (iii) Hence, determine
J
=
∫
0
1
[
2
sin
(
5
x
−
2
)
+
3
e
7
x
+
1
]
d
x
J=\displaystyle \int_{0}^{1}\bigl[2\sin(5x-2)+3e^{7x+1}\bigr]dx
J
=
∫
0
1
[
2
sin
(
5
x
−
2
)
+
3
e
7
x
+
1
]
d
x
.
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