Find EXACT area of two equations intergration?

Question

find EXACT area with these 2 equations
#y^2=x# and #x-y=2#
so u rearrange so get y= so:
y=-2+x
i dont know how to get y^2=x just by y

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Answer 1 · 2018-05-02T12:50:04

#"Area"=4.5#

Rearrange to get:
#x=y^2# and #x=y+2#

We need the points of intersection:
#y^2=y+2#
#y^2-y-2=0#
#(y+1)(y-2)=0#

#y=-1# or #y=2#

Our bounds are #-1# and #2#

#"Area"=int_(-1)^2y+2dy-int_(-1)^2y^2dy#

#=[y^2/2+2y]_text(-1)^2-[y^3/3]_text(-1)^2#

#=[(2^2/2+2(2))-((-1)^2/2+2(-1))]-[(2^3/3)-((-1)^3/3)]#

#=[6+3/2]-[8/3+1/3]#

#=15/2-9/3#

#=7.5-3#

#=4.5#