Area Between Curves?

Question

#y=x^2#
#y=2-x^2#
#y=2x+8#

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Answer 1 · 2018-06-14T08:33:39

#=100/3# Squared Units

by checking the graph You see you want the area surrounded by the three curves.

First, you get the points of intersection of,

#color(green)((1)#straight line and the curve #y=x^2#

#(-2,4),(4,16)#

#color(green)((2)# the two curves

#(-1,1),(1,1)#

First, You get the area between the straight line and the curve #x^2# and then subtract from it the area between the two curves

#color(green)("Area"=int_a^b(y_2-y_1)dx#

Substitute with the given functions

Area #=int_-2^4(2x+8-x^2)dx-int_-1^1(2-x^2-x^2)dx#

#=([x^2+8x-x^3/3]_-2^4)#

#-([2x-(2x^3)/3]_-1^1)#

#=100/3# Squared Units