Question

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

Answer 1

hola there
answer in the picture

Answer 2

The area of the region bounded by the line x-y+2=0 and x=root y and y axis is 10/3

• x=root y implies y=x^2. Now we have to first find the point of intersection of these two curves.
• putting y=x^2 in the line x-y+2=0 we get x^2-x-2 =0
• Factoring it we get (x-2)(x+1) = 0 which implies x=2 or x= - 1
• now as x>=0 we ignore the second value and take the value x=2. Hence the point of intersection is (2,4)

• Now the required area is $\int\limits^2_0 {(x+2-x^{2}) } \, dx$

• Evaluating the integral we get $[\frac{x^{2} }{2} +2x - x^{2} ]$ with limits 0 to 2
• This on simplification evaluates to 10/3