a.
`"Required area "=2int_(0)^(1)x|x|dx`
`=2((x^(3))/(3))_(0)^(1)=(2)/(3)`
b.
`"Required area "=int_(0)^(2)[(x+2)]-(x^(2))]dx=[(x^(2))/(2)+2x-(x^(3))/(3)]_(0)^(2)`
`=2+4-(8)/(3)=(10)/(3)` sq. units.
c. `"Reqd. area "=int_(0)^(1)(sqrt(x)-x)dx=[(x^(3//2))/(3//2)-(x^(2))/(2)]_(0)^(1)`
`=((1)/(3//2)-(1)/(2))=(2)/(3)-(1)/(2)=(1)/(6)` sq. units.
d. `y=4" meet the parabola "y^(2)=x" at "A" is "(16,4)`
Required area= Area of rectangle OMAC-Area OMA
`=4xx16-int_(0)^(16)sqrt(x)dx=64-|(x^(3//2))/(3//2)|_(0)^(16)`
`=64-(2)/(3)(4)^(3)`
`=64-(128)/(3)=(64)/(3)` sq. units.
