What is the integral from 0 to 1 of pix ?

The integral from 0 to 1 of pix is pi/2

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integral from 0 to 1 of pix

\int_{0}^{1} π x d x

\frac{π}{2}

Decimal Notation

1.57079 \dots

Solution steps

\int_{0}^{1} π x d x

Take the constant out:

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

= π \cdot \int_{0}^{1} x d x

Apply the Power Rule

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

= π [\frac{x ^{2}}{2}]_{0}^{1}

Compute the boundaries:

\frac{1}{2}

= π \frac{1}{2}

Simplify

= \frac{π}{2}

\int_{0}^{9} \frac{x}{x ^{2} + 1} d x

\int_{- π}^{0} - x cos (n x) d x

\int_{1}^{2} 2 x^{3} d x

\int_{- 4}^{4} 4^{2} - x^{2} d x

\int_{2}^{2} x d x

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