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}^{1} \frac{1 - x}{x} d x

\int_{\frac{2 π}{3}}^{π} cos (\frac{x}{2}) d x

\int_{0}^{\infty} x e^{- 6 x} d x

\int_{3}^{7} 2 d x

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