Answer to Question #186627 in Calculus for Jethro

Question #186627

Determine the area of the region bounded by:


1.) y = x2, y = 2x + 3


2.) x² = y - 1, x = y - 3


3.) y = x², y = 2 - x²


1
Expert's answer
2021-05-07T10:17:37-0400

Solution:-


1.)

y = x2, y = 2x + 3

on solving

"x^2 -2x - 3 = 0"

"x = -1 , 3"

so ,


"\\intop _{-1}^{3}(3 + 2x - x^2) dx"


= "\\frac {32} {3}"

= "10.66 \\ answer"

2.) x² = y - 1, x = y - 3


on solving

"2 + x - x^2= 0"


"x = -1 , 2"

so,


"\\intop _{-1}^{2}(2 + x - x^2) dx"


"= \\frac {9} {2}"


"= 4.5 \\ answer"



3.) y = x², y = 2 - x²


on solving


"2- 2x^2 =0"


"x =-1 , 1"


so ,


"\\intop _{-1}^{1}(2 - 2x^2) dx"


"= \\frac {8} {3}"


"= 2.66 \\ answer"


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