What is the integral from 1 to 6 of 8x ?

The integral from 1 to 6 of 8x is 140

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integral from 1 to 6 of 8x

\int_{1}^{6} 8 x d x

140

Solution steps

\int_{1}^{6} 8 x d x

Take the constant out:

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

= 8 \cdot \int_{1}^{6} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{1}^{6}

= 8 [\frac{x ^{2}}{2}]_{1}^{6}

Compute the boundaries:

\frac{35}{2}

= 8 \cdot \frac{35}{2}

Simplify

= 140

\frac{5 x}{1 + x ^{2}}

\frac{\partial}{\partial x} (x y + x)

\frac{d}{d x} (- 2 sin (x) + 2 sin (2 x))

\int (cos (x) - sec (x)) d x

(t + 5)^{\frac{2}{3}} (3 t^{2} - 2)^{3}