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icang [17]
3 years ago
6

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

Mathematics
1 answer:
erastova [34]3 years ago
8 0

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}

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