Question
Find the area bounded by y = |x| and y = 6 −x^2.
Answers
mathhelper
y = |x| ---> y = x or x = -x
sketch this along with the parabola.
Due to the nice symmetry, need the area between y = x and y = 6-x^2
in the first quadrant, then double this answer.
area in quad I = ∫ (6 - x^2 - x) dx from 0 to 2
= [6x - (1/3)x^3 - (1/2)x^2 ] from 0 to 2
= 12 - 8/3 - 2 - 0
= 10 - 8/3
= 22/3
so the total area = 2(22/3) = 44/3
sketch this along with the parabola.
Due to the nice symmetry, need the area between y = x and y = 6-x^2
in the first quadrant, then double this answer.
area in quad I = ∫ (6 - x^2 - x) dx from 0 to 2
= [6x - (1/3)x^3 - (1/2)x^2 ] from 0 to 2
= 12 - 8/3 - 2 - 0
= 10 - 8/3
= 22/3
so the total area = 2(22/3) = 44/3