What is area y=7x^2,y^2= 1/7 x ?

The answer to area y=7x^2,y^2= 1/7 x is 1/147

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area y=7x^2,y^2= 1/7 x

area

y = 7 x^{2}, y^{2} = \frac{1}{7} x

\frac{1}{147}

Decimal Notation

0.00680 \dots

Solution steps

Isolate

y

for

y^{2} = \frac{1}{7} x : y = \frac{x}{7}, y = - \frac{x}{7}

f_{1} (x) = 7 x^{2}

f_{2} (x) = \frac{x}{7}

To find the intersection points solve

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

7 x^{2} = \frac{x}{7} : x = 0, x = \frac{1}{7}

7 x^{2} = - \frac{x}{7} : x = 0

\frac{x}{7} = - \frac{x}{7} : x = 0

= \int_{0}^{\frac{1}{7}} ∣ f_{1} (x) - f_{2} (x) ∣ d x

= \int_{0}^{\frac{1}{7}} 7 x^{2} - \frac{x}{7} d x

\int_{0}^{\frac{1}{7}} 7 x^{2} - \frac{x}{7} d x = \frac{1}{147}

= \frac{1}{147}

\frac{1}{1 + x}

x \to 3 + lim (x^{2})

\int \frac{1}{x ^{3} + 3 x ^{2}} d x

y^{^{''}} - y^{^{'}} - 2 y = - 6 t + 10 t^{2}

\frac{1 + e ^{- s π}}{s ^{2} + 1}