Find the exact area enclosed between the curve y=sqrt(4-x^2) and the line x-y+2=0
- print Print
- list Cite
Expert Answers
calendarEducator since 2011
write5,348 answers
starTop subjects are Math, Science, and Business
You first need to find the interception points between the curves, hence, you should solve the system of equations `y=x+2` and `y=sqrt(4-x^2)` such that:
`x+2 = sqrt(4-x^2)`
You need to raise to square to remove the square root such that:
`(x+2)^2 = 4 - x^2`
You need to expand the binomial such that:
`x^2 + 4x + 4 = 4 - x^2`
You need to move all terms to the left side such that:
`x^2 + 4x + 4 - 4 + x^2 = 0`
`2x^2 + 4x = 0`
Factoring out 2x yields:
`2x(x + 2) = 0 =gt x = 0 and x+2 = 0 =gt x = -2`
You need to verify what is the upper limit curve and what is the lower limit curve, between -2 and 0 values, hence, you should select the value -1 to evaluate both functions such that:
`y = -1+2 = 1`
`sqrt(4 - 1) = sqrt 3`
Notice that sqrt>1, hence the...
(The entire section contains 403 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
- Sketch the region enclosed by the given curves. y = 4 cos 2x, y = 4 − 4 cos 2x, 0 ≤ x ≤ π/2...
- 1 Educator Answer
- Calculate the area enclosed by y = X^2 and y = x + 2.
- 1 Educator Answer
- Find the exact area bounded by the curves y=sinx and y=cosx in the domain 0≤x≤2pi
- 1 Educator Answer
- `y = sqrt(x), y = (1/2)x, x = 9` Sketch the region enclosed by the given curves and find its...
- 1 Educator Answer