What is the integral from-1 to 3 of (2x)^3 ?

The integral from-1 to 3 of (2x)^3 is 160

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integral from-1 to 3 of (2x)^3

\int_{- 1}^{3} (2 x)^{3} d x

160

Solution steps

\int_{- 1}^{3} (2 x)^{3} d x

Simplify

(2 x)^{3} : 8 x^{3}

= \int_{- 1}^{3} 8 x^{3} d x

Take the constant out:

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

= 8 \cdot \int_{- 1}^{3} x^{3} d x

Apply the Power Rule

: [\frac{x ^{4}}{4}]_{- 1}^{3}

= 8 [\frac{x ^{4}}{4}]_{- 1}^{3}

Compute the boundaries:

20

= 8 \cdot 20

Simplify

= 160

(7) (0 - 6)

x^{4} + y^{3} x^{5} + 2 y^{^{'}} = 0

\frac{\partial}{\partial x} (x^{3} + y)

f (x) = 2 x^{2} + 1, (1, 3)

\frac{d}{d x} (x ln (x^{2} + 5))

What is the integral from-1 to 3 of (2x)^3 ?
The integral from-1 to 3 of (2x)^3 is 160