y= x^2
y= x+2
To find the area will need to find the integral for both equations:
First we need to determine the intersecting points:
==> x^2 = x+ 2
==> x^2 -x -2 = 0
==> (x-2)(x+1) = 0
==> x= 2 x = -1
Then we need to...
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find the integral from x= -1 to x= 2
First let us find the area under y= x^2 from x= -1 to 2
==> A1 = intg ( x^2 ) dx
= x^3/3
= ( 2^3/3) - (-1)^3 / 3
= ( 8 + 1)/3 = 9/3 = 3
Then the area under y=x^2 from (-1 to 2 ) is 3 square units>
Now we will calculate the area under y= x+2:
A2 = intg (x+ 2)
= x^2/2 + 2x
= ( 2^2/2 + 2*2) - ( -1^2/2 + 2*-1)
= 2 + 4) - ( 1/2 - 2)
= 6 + 3/2 = 15/2 = 7.5 square units:
Then the area is:
A = A2 - A1 = 7.5 - 3 = 4.5
Then, the area between y= x^2 and y= x+2 is 4.5 square units