What is the integral from 5 to 7 of [ k/2 x^2] ?

The integral from 5 to 7 of [ k/2 x^2] is (109k)/3

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integral from 5 to 7 of [ k/2 x^2]

\int_{5}^{7} [\frac{k}{2} x^{2}] d x

\frac{109 k}{3}

Solution steps

\int_{5}^{7} \frac{k}{2} x^{2} d x

Take the constant out:

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

= \frac{k}{2} \cdot \int_{5}^{7} x^{2} d x

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{5}^{7}

= \frac{k}{2} [\frac{x ^{3}}{3}]_{5}^{7}

Compute the boundaries:

\frac{218}{3}

= \frac{k}{2} \cdot \frac{218}{3}

Simplify

= \frac{109 k}{3}

y^{^{''}} + 5 y^{^{'}} = e^{- t}, y (0) = 0, y^{^{'}} (0) = 1

\frac{\partial}{\partial y} (e^{x y} ln (z))

\int \frac{( ln ( 2 x ) )}{x} d x

x \to 4 lim (f (x))

f (x) = - \frac{1}{x}

What is the integral from 5 to 7 of [ k/2 x^2] ?
The integral from 5 to 7 of [ k/2 x^2] is (109k)/3