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Mathematics
Mathematics
Problem
Consider the integral
I
=
∫
0
ln
2
3
e
3
x
sin
(
e
3
x
)
d
x
.
I=\displaystyle \int_{0}^{\ln 2} 3e^{3x}\,\sin\bigl(e^{3x}\bigr)\,dx.
I
=
∫
0
l
n
2
3
e
3
x
sin
(
e
3
x
)
d
x
.
a. (i) Find the indefinite integral
∫
3
e
3
x
sin
(
e
3
x
)
d
x
.
\displaystyle \int 3e^{3x}\,\sin\bigl(e^{3x}\bigr)\,dx.
∫
3
e
3
x
sin
(
e
3
x
)
d
x
.
b. (ii) Hence, evaluate
I
.
I.
I
.
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