What is area y=10x^2,y^2= 1/10 x ?

The answer to area y=10x^2,y^2= 1/10 x is 1/300

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area y=10x^2,y^2= 1/10 x

area

y = 10 x^{2}, y^{2} = \frac{1}{10} x

\frac{1}{300}

Decimal

0.00333 \dots

Solution steps

Isolate

y

for

y^{2} = \frac{1}{10} x : y = \frac{x}{10}, y = - \frac{x}{10}

f_{1} (x) = 10 x^{2}

f_{2} (x) = \frac{x}{10}

To find the intersection points solve

f_{i} (x) = f_{j} (x)

10 x^{2} = \frac{x}{10} : x = 0, x = \frac{1}{10}

10 x^{2} = - \frac{x}{10} : x = 0

\frac{x}{10} = - \frac{x}{10} : x = 0

= \int_{0}^{\frac{1}{10}} ∣ f_{1} (x) - f_{2} (x) ∣ d x

= \int_{0}^{\frac{1}{10}} 10 x^{2} - \frac{x}{10} d x

\int_{0}^{\frac{1}{10}} 10 x^{2} - \frac{x}{10} d x = \frac{1}{300}

= \frac{1}{300}

What is area y=10x^2,y^2= 1/10 x ?
The answer to area y=10x^2,y^2= 1/10 x is 1/300