What is the integral from 0 to 1 of 2pix ?

The integral from 0 to 1 of 2pix is pi

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integral from 0 to 1 of 2pix

\int_{0}^{1} 2 π x d x

π

Decimal Notation

3.14159 \dots

Solution steps

\int_{0}^{1} 2 π 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 d x

Apply the Power Rule

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

= 2 π [\frac{x ^{2}}{2}]_{0}^{1}

Compute the boundaries:

\frac{1}{2}

= 2 π \frac{1}{2}

Simplify

= π

\int_{0}^{4} x x^{2} + 7 d x

\int_{\frac{1}{2}}^{1} x^{2} ln (x) d x

\int_{0}^{\infty} e^{x^{2}} d x

\int_{0}^{1} 7 cos (\frac{π x}{2}) d x

\int_{0}^{2} \frac{2 x}{( x - 3 ) ^{2}} d x

What is the integral from 0 to 1 of 2pix ?
The integral from 0 to 1 of 2pix is pi