# Y=sqrt(x), y=0, x=0,and x=2 a. Find the area of the region b. find the volume of the solid formed by rotating the region about the x-axis c. find the volume of the solid?

Apr 23, 2018

Show below

#### Explanation:

a)

$A = {\int}_{0}^{2} \sqrt{x} \cdot \mathrm{dx}$

$A = {\left[{x}^{\frac{3}{2}}\right]}_{0}^{2} = \sqrt{8}$

b)

$v o l u m e = {\int}_{0}^{2} \pi \cdot {y}^{2} \cdot \mathrm{dx}$

$v o l u m e = {\int}_{0}^{2} \pi \cdot x \cdot \mathrm{dx} = \frac{1}{2} \pi {\left[{x}^{2}\right]}_{0}^{2} = 2 \pi$

c)This command doesnot complete

this is the sketch of the function.