Question
Find the area of the region bounded by the curves y=x^2 - 2x and y= x + 4
Answers
Reiny
did you find their points of intersection?
x^2 - 2x = x+4
x^2 - 3x - 4= 0
(x-4)(x+1) = 0
x = -1 or x = 4
effective height of region = x+4 - (x^2 - 2x)= 3x + 4 - x^2
area = [integral] (3x + 4 - x^2) dx from -1 to 4
= [(3/2)x^2 + 4x - (1/3)x^3] from -1 to 4
I will leave the arithmetic up to you
x^2 - 2x = x+4
x^2 - 3x - 4= 0
(x-4)(x+1) = 0
x = -1 or x = 4
effective height of region = x+4 - (x^2 - 2x)= 3x + 4 - x^2
area = [integral] (3x + 4 - x^2) dx from -1 to 4
= [(3/2)x^2 + 4x - (1/3)x^3] from -1 to 4
I will leave the arithmetic up to you