What is area y=6x^2,y^2= 1/6 x ?

The answer to area y=6x^2,y^2= 1/6 x is 1/108

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area y=6x^2,y^2= 1/6 x

area

y = 6 x^{2}, y^{2} = \frac{1}{6} x

\frac{1}{108}

Decimal Notation

0.00925 \dots

Solution steps

Isolate

y

for

y^{2} = \frac{1}{6} x : y = \frac{x}{6}, y = - \frac{x}{6}

f_{1} (x) = 6 x^{2}

f_{2} (x) = \frac{x}{6}

To find the intersection points solve

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

6 x^{2} = \frac{x}{6} : x = 0, x = \frac{1}{6}

6 x^{2} = - \frac{x}{6} : x = 0

\frac{x}{6} = - \frac{x}{6} : x = 0

= \int_{0}^{\frac{1}{6}} ∣ f_{1} (x) - f_{2} (x) ∣ d x

= \int_{0}^{\frac{1}{6}} 6 x^{2} - \frac{x}{6} d x

\int_{0}^{\frac{1}{6}} 6 x^{2} - \frac{x}{6} d x = \frac{1}{108}

= \frac{1}{108}

y^{^{''}} + 4 y = - 4 sin (2 t)

\int \frac{2 x}{x ^{2} + 4} d x

\frac{d}{d x} (sin ((π x)^{3}))

(2 x + 1)^{4}

x \to \infty lim (lo g_{2} (\frac{( x + 2 )}{( 2 \cdot x + 1 )}))