Find the Area Of the Region
- Thread starter KEYWEST17
- Start date
I assume the shaded region is the area in question?.
Find the area under \(\displaystyle e^{2x}\) from 0 to 1:
\(\displaystyle \int_{0}^{1}e^{2x}dx\)
Find the area under \(\displaystyle e^{6x}\) from \(\displaystyle -\infty \;\ \text{to} \;\ 0\):
\(\displaystyle \int_{-\infty}^{0}e^{6x}dx\)
Add them up.
This is assuming my assessment is correct and I have the correct region as in the diagram.
But, if you need the region between the two e functions: \(\displaystyle \int_{-\infty}^{0}\left[e^{2x}-e^{6x}\right]dx\)
Find the area under \(\displaystyle e^{2x}\) from 0 to 1:
\(\displaystyle \int_{0}^{1}e^{2x}dx\)
Find the area under \(\displaystyle e^{6x}\) from \(\displaystyle -\infty \;\ \text{to} \;\ 0\):
\(\displaystyle \int_{-\infty}^{0}e^{6x}dx\)
Add them up.
This is assuming my assessment is correct and I have the correct region as in the diagram.
But, if you need the region between the two e functions: \(\displaystyle \int_{-\infty}^{0}\left[e^{2x}-e^{6x}\right]dx\)
Attachments
I am unsure of what region you are looking for.
Is it \(\displaystyle \int_{0}^{1}e^{2x}dx\)?.
Or
\(\displaystyle \int_{-\infty}^{0}\left(e^{2x}-e^{6x}\right)dx\)?.
Or both?.
Or something else?.
The problem may indicate both.
\(\displaystyle \int_{-\infty}^{0}\left(e^{2x}-e^{6x}\right)dx+\int_{0}^{1}e^{2x}dx\)
Show us what you're doing so we can pinpoint the trouble.
Is it \(\displaystyle \int_{0}^{1}e^{2x}dx\)?.
Or
\(\displaystyle \int_{-\infty}^{0}\left(e^{2x}-e^{6x}\right)dx\)?.
Or both?.
Or something else?.
The problem may indicate both.
\(\displaystyle \int_{-\infty}^{0}\left(e^{2x}-e^{6x}\right)dx+\int_{0}^{1}e^{2x}dx\)
Show us what you're doing so we can pinpoint the trouble.