using integration find the area of the region bounded by the line x-y+2=0, the curve x=y^1/2 and y axis - Maths - Application of Integrals

Question

using integration find the area of the region bounded by the line
x-y+2=0, the curve x=y^1/2 and y axis

Akhil Goyal · Accepted Answer

The diagram
will look as shown below We need to find area of the shaded (green)
region
<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/ck-files/ck_550d63dca5aab%20png">
Required area (A)=∫0a(x+2)-x2dxFirst we need to get 'a'This represent the point of intersection of the two curves, so we equate the two functions:x+2=x2⇒x2-x-2=0⇒x2-2x+x-2=0⇒(x-2)(x+1)=0since x>0, we reject the solution x=-1Hence, a=2So:A=∫02(x+2)-x2dx=x22+2x-x3302=2+4-83=103

using integration find the area of the region bounded by the line x-y+2=0, the curve x=y^1/2 and y axis.