What is the integral from 0 to 1 of 2pix(sqrt(x)) ?

The integral from 0 to 1 of 2pix(sqrt(x)) is (4pi)/5

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integral from 0 to 1 of 2pix(sqrt(x))

\int_{0}^{1} 2 π x (x) d x

\frac{4 π}{5}

Decimal Notation

2.51327 \dots

Solution steps

\int_{0}^{1} 2 π x x d x

Take the constant out:

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

= 2 π \cdot \int_{0}^{1} x x d x

Simplify

x x : x^{\frac{3}{2}}

= 2 π \cdot \int_{0}^{1} x^{\frac{3}{2}} d x

Apply the Power Rule

: [\frac{2}{5} x^{\frac{5}{2}}]_{0}^{1}

= 2 π [\frac{2}{5} x^{\frac{5}{2}}]_{0}^{1}

Compute the boundaries:

\frac{2}{5}

= 2 π \frac{2}{5}

Simplify

= \frac{4 π}{5}

\int \frac{2}{9} \frac{x ^{2}}{x ^{5}} d x

\int \frac{1}{( x + 1 ) ( x + 2 ) ( x + 3 )} d x

\frac{\partial}{\partial x} (9 - x^{2} + x y - 4 y^{2})

\int \frac{1}{cos ( x ) - 1} d x

x \to 0 lim (\frac{5 ^{x} - 1}{x})

What is the integral from 0 to 1 of 2pix(sqrt(x)) ?
The integral from 0 to 1 of 2pix(sqrt(x)) is (4pi)/5