What is the integral from 0 to 4 of |x^2-5| ?

The integral from 0 to 4 of |x^2-5| is 10sqrt(5)+(-10sqrt(5)+64)/3-20

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integral from 0 to 4 of |x^2-5|

\int_{0}^{4} x^{2} - 5 d x

105 + \frac{- 10 5 + 64}{3} - 20

Decimal Notation

16.24045 \dots

Solution steps

\int_{0}^{4} x^{2} - 5 d x

Eliminate Absolutes

= \int_{0}^{5} - x^{2} + 5 d x + \int_{5}^{4} x^{2} - 5 d x

\int_{0}^{5} - x^{2} + 5 d x = - \frac{5 5}{3} + 55

\int_{5}^{4} x^{2} - 5 d x = \frac{64 - 5 5}{3} - 20 + 55

= - \frac{5 5}{3} + 55 + \frac{64 - 5 5}{3} - 20 + 55

Simplify

- \frac{5 5}{3} + 55 + \frac{64 - 5 5}{3} - 20 + 55 : 105 + \frac{- 10 5 + 64}{3} - 20

= 105 + \frac{- 10 5 + 64}{3} - 20

\int_{4}^{16} (y - \frac{y}{4}) d y

\int_{2}^{4} \frac{1}{4} d x

\int_{1}^{4} (x^{2} + 2 x) d x

\int_{0}^{4} 15 - 2 x - 7 d x

\int_{1}^{4} \frac{1 + t}{t} d t

What is the integral from 0 to 4 of |x^2-5| ?
The integral from 0 to 4 of |x^2-5| is 10sqrt(5)+(-10sqrt(5)+64)/3-20