Question

Find the area bounded by the curve y = x1/2 + 2 the x - axis, and the lines x = 1 and x = 4?

A.7 1/2. B.10 2/3 C.16 D. 28 1/2

Answer 1

The area is given by


`\displaystyle\int_1^4(x^(1/2)+2)\,\mathrm dx=\left(\frac23x^(3/2)+2x\right)\bigg|_(x=1)^(x=4)=\frac{40}3-\frac83=\frac{32}3=10+\frac23`

so the answer is B