Ratios are proportional if they represent the same relationship. One way to see if two ratios are proportional is to write them as fractions and then reduce them. If the reduced fractions are the same, your ratios are proportional.

3 0

3 years ago

What is the area of the region bounded between the curves y=x and y=sqrt(x)?

erastova [34]

Answer:

$\frac{1}{6}$

Step-by-step explanation:

y = x .....(1)

$y=\sqrt{x}$ .... (2)

By solving equation (1) and equation (2)

$x = \sqrt{x}$

$\sqrt{x}\left ( \sqrt{x}-1 \right )=0$

$\sqrt{x}=0$ or $\left ( \sqrt{x}-1 \right )=0$

x = 0, x = 1

y = 0, y = 1

A = $\int_{0}^{1}ydx(curve)-\int_{0}^{1}ydx(line)$

A = $\int_{0}^{1}\sqrt{x}dx-\int_{0}^{1}xdx$

A = $\frac{2}{3}[x^\frac{3}{2}]_{0}^{1}-\frac{1}{2}[x^2]_{0}^{1}$

A = $\frac{2}{3}-\frac{1}{2}$

A = $\frac{1}{6}$

8 0

3 years ago