Question

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

Answer 1

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 ,

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

$= \frac {8} {3}$

$= 2.66 \ answer$