Question

How do you get 3/2(5-e) from that?

Answer 1

Find the integration of:
\[\int\limits_{0}^{\ln2}(5e ^{2x} - e ^{2x+1})dx\]

Answer 2

from here i get:

Answer 3

\[[\frac{ 5 }{ 2 }e ^{2x} - \frac{ 1 }{ 2 }e ^{2x+1}]\]

Answer 4

evaluated from 0 to ln2

Answer 5

then obviously i just plug and chug but when i do, I get a different answer that what's on the book.

Answer 6

\[\int(5e^{2x}-e^{2x+1})dx = \frac{5e^{2x}}{2}-\frac{e^{2x+1}}{2}\]
\[(\frac{5e^{2\ln 2}}{2}-\frac{e^{2 ln 2+1}}{2})-(\frac{5e^{0}}{2}-\frac{e^{0+1}}{2})\]\[=\frac{20}{2}-\frac{4e}{2}-\frac{5}{2}+\frac{e}{2} = \frac{15}{2}-\frac{3e}{2} = \frac{3}{2}(5-e)\]

Answer 7

\[2\ln 2 = \ln 4\]\[e^{\ln 4}=4\] \[e^{\ln 4 +1} = e^{\ln 4 } * e = 4e\]