Find the region enclosed by the curves: `y=e^(x)` , `y=xe^(x)` , x=0``
- print Print
- list Cite
Expert Answers
Luca B.
| Certified Educator
calendarEducator since 2011
write5,348 answers
starTop subjects are Math, Science, and Business
You need to find the limits of integration, hence, you need to solve the equation `e^x = x*e^x` , such that:
`e^x = x*e^x => e^x - x*e^x = 0`
Factoring out` e^x` yields:
`e^x(1 - x) = 0`
Since `e^x > 0` , hence `1 - x = 0 => x = 1`
You need to evaluate the functions `y = e^x` and `y = x*e^x` at `x = 0` and `x = 1/2` , such that:
`x = 0 => y = e^0 => y = 1`
`x = 0 => y = 0*e^0 = 0`
`x = 1/2 => y = e^(1/2) => y = sqrt e `
`x = 1/2 => y =...
(The entire section contains 298 words.)
Unlock This Answer Now
Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.
Related Questions
- `x = y^4, y = sqrt(2 - x), y = 0` Sketch the region enclosed by the given curves and find...
- 1 Educator Answer
- `y = cos(x), y = 1 - cos(x), 0<=x<=pi` Sketch the region enclosed by the given curves...
- 1 Educator Answer
- Sketch the region enclosed by the given curves. y = 4 cos 2x, y = 4 − 4 cos 2x, 0 ≤ x ≤ π/2...
- 1 Educator Answer
- `y = x^2, y = 4x - x^2` Sketch the region enclosed by the given curves and find its area.
- 1 Educator Answer
- `y = 12 - x^2, y = x^2 - 6` Sketch the region enclosed by the given curves and find its area.
- 1 Educator Answer