What is the integral from 0 to 4 of 14(600+20x^2) ?

The integral from 0 to 4 of 14(600+20x^2) is 118720/3

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integral from 0 to 4 of 14(600+20x^2)

\int_{0}^{4} 14 (600 + 20 x^{2}) d x

\frac{118720}{3}

Decimal Notation

39573.33333 \dots

Solution steps

\int_{0}^{4} 14 (600 + 20 x^{2}) d x

Take the constant out:

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

= 14 \cdot \int_{0}^{4} 600 + 20 x^{2} 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

= 14 (\int_{0}^{4} 600 d x + \int_{0}^{4} 20 x^{2} d x)

\int_{0}^{4} 600 d x = 2400

\int_{0}^{4} 20 x^{2} d x = \frac{1280}{3}

= 14 (2400 + \frac{1280}{3})

Simplify

14 (2400 + \frac{1280}{3}) : \frac{118720}{3}

= \frac{118720}{3}

\int_{- 2}^{4} (3 x^{2} - 4 x + 5) d x

\int_{- 6}^{6} 6 - ∣ x ∣ d x

\int_{0}^{2} 4^{3 x} d x

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

What is the integral from 0 to 4 of 14(600+20x^2) ?
The integral from 0 to 4 of 14(600+20x^2) is 118720/3