What is the integral from 0 to 3 of 2pi(x+7)(2x) ?

The integral from 0 to 3 of 2pi(x+7)(2x) is 162pi

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integral from 0 to 3 of 2pi(x+7)(2x)

\int_{0}^{3} 2 π (x + 7) (2 x) d x

162 π

Decimal

508.93800 \dots

Solution steps

\int_{0}^{3} 2 π (x + 7) \cdot 2 x d x

Take the constant out:

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

= 2 π 2 \cdot \int_{0}^{3} (x + 7) x d x

Simplify

= 4 π \cdot \int_{0}^{3} (x + 7) x d x

Expand

(x + 7) x : x^{2} + 7 x

= 4 π \cdot \int_{0}^{3} x^{2} + 7 x d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 4 π (\int_{0}^{3} x^{2} d x + \int_{0}^{3} 7 x d x)

\int_{0}^{3} x^{2} d x = 9

\int_{0}^{3} 7 x d x = \frac{63}{2}

= 4 π (9 + \frac{63}{2})

Simplify

4 π (9 + \frac{63}{2}) : 162 π

= 162 π

y^{^{''}} + y = cos (x)

f (x) = x^{3} - 27 x

\frac{d}{d x} (x^{x l n (x)})

\int e^{- p x} d x

(7 x^{6} + 8 x^{3})^{4}

What is the integral from 0 to 3 of 2pi(x+7)(2x) ?
The integral from 0 to 3 of 2pi(x+7)(2x) is 162pi