What is the integral from 0 to 1 of 2pix\sqrt[3]{x} ?

The integral from 0 to 1 of 2pix\sqrt[3]{x} is (6pi)/7

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integral from 0 to 1 of 2pix\sqrt[3]{x}

\frac{6 π}{7}

Decimal Notation

2.69279 \dots

Solution steps

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

Apply Integration By Parts

\int \frac{1}{6} x^{\frac{4}{3}} d x = \frac{1}{14} x^{\frac{7}{3}}

Simplify

Compute the boundaries:

\frac{3}{7}

= 2 π \frac{3}{7}

Simplify

= \frac{6 π}{7}

\frac{d}{d x} (8 x^{5} 2 π)

\int_{1}^{4} \frac{x ^{2} + 4}{x} d x

\frac{d}{d x} (\frac{x ^{2} + 6}{( 2 x - 7 ) ^{7}})

x \to 0 lim (\frac{200 π}{x})

y = \frac{y + 5 x}{3 y - x}, (1, 2)

What is the integral from 0 to 1 of 2pix\sqrt[3]{x} ?
The integral from 0 to 1 of 2pix\sqrt[3]{x} is (6pi)/7