What is the integral from 0 to x of kx ?

The integral from 0 to x of kx is (kx^2)/2

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integral from 0 to x of kx

\int_{0}^{x} k x d x

\frac{k x ^{2}}{2}

Solution steps

\int_{0}^{x} k x d x

Take the constant out:

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

= k \cdot \int_{0}^{x} x d x

Apply the Power Rule

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

= k [\frac{x ^{2}}{2}]_{0}^{x}

Compute the boundaries:

\frac{x ^{2}}{2}

= k \frac{x ^{2}}{2}

Simplify

= \frac{k x ^{2}}{2}

\int_{0}^{π} x cos (2 x^{2}) d x

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\int_{0}^{π} cos (x) x d x

\int_{π}^{0} cos (x) d x

\int_{1}^{8} 4 x^{\frac{1}{3}} d x

What is the integral from 0 to x of kx ?
The integral from 0 to x of kx is (kx^2)/2