What is the integral from 1 to 4 of sqrt(16x^5) ?

The integral from 1 to 4 of sqrt(16x^5) is 1016/7

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integral from 1 to 4 of sqrt(16x^5)

\int_{1}^{4} 16 x^{5} d x

\frac{1016}{7}

Decimal Notation

145.14285 \dots

Solution steps

\int_{1}^{4} 16 x^{5} d x

16 x^{5} = 16 x^{5}

= \int_{1}^{4} 16 x^{5} d x

Take the constant out:

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

= 16 \cdot \int_{1}^{4} x^{5} d x

16 = 4

= 4 \cdot \int_{1}^{4} x^{5} d x

x^{5} = x^{\frac{5}{2}},

assuming

x \geq 0

= 4 \cdot \int_{1}^{4} x^{\frac{5}{2}} d x

Apply the Power Rule

: [\frac{2}{7} x^{\frac{7}{2}}]_{1}^{4}

= 4 [\frac{2}{7} x^{\frac{7}{2}}]_{1}^{4}

Compute the boundaries:

\frac{254}{7}

= 4 \cdot \frac{254}{7}

Simplify

= \frac{1016}{7}

\frac{d y}{d x} = - 2 x (y - 3)

y^{^{''}} - 4 y^{^{'}} + 3 y = x, y (0) = 1, y^{^{'}} (0) = 0

\int_{1}^{e} \frac{8}{z}

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

What is the integral from 1 to 4 of sqrt(16x^5) ?
The integral from 1 to 4 of sqrt(16x^5) is 1016/7