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
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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