Find the area of the following domains in \( X Y \)-plane bounded by the indicated curves
1. \( y=x, y=x^{2} \)
Ans. \( \frac{1}{6} \)
2. \( y=3 x-x^{2}, y=x \)
Ans. \( \frac{4}{3} \)
3. \( 3 x=4-y^{2}, x=y^{2} \)
Hint: Easy to integrate with, limits: \( x: y^{2} \) to \( \left(4-y^{2}\right) / 3, y:-1 \) to 1 .
Ans. \( \frac{16}{9} \)
4. \( y=x^{2} \) and \( y=x+2 \)
Hint: Easy to integrate with
limits: \( y: x^{2} \) to \( x+2 ; x:-1 \) to 2 .
