What is the integral from 0 to 4 of (4x^2+7x) ?

The integral from 0 to 4 of (4x^2+7x) is 424/3

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integral from 0 to 4 of (4x^2+7x)

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

\frac{424}{3}

Decimal Notation

141.33333 \dots

Solution steps

\int_{0}^{4} 4 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

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

\int_{0}^{4} 4 x^{2} d x = \frac{256}{3}

\int_{0}^{4} 7 x d x = 56

= \frac{256}{3} + 56

Simplify

\frac{256}{3} + 56 : \frac{424}{3}

= \frac{424}{3}

\frac{d}{d x} (e^{x} x^{3})

\frac{d y}{d x} = (\frac{( 2 y + 7 )}{( 8 x + 9 )})^{2}

\frac{s ( s + 2 )}{( s + 1 ) ^{2}}

\int \frac{1}{e ^{y} sin ^{2} ( e ^{- y} )} d y

f (x) = \frac{1}{x ^{7} + 2}

What is the integral from 0 to 4 of (4x^2+7x) ?
The integral from 0 to 4 of (4x^2+7x) is 424/3