What is the integral from 0 to 4 of |2x^2-7x+3| ?

The integral from 0 to 4 of |2x^2-7x+3| is 109/12

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integral from 0 to 4 of |2x^2-7x+3|

\int_{0}^{4} 2 x^{2} - 7 x + 3 d x

\frac{109}{12}

Decimal Notation

9.08333 \dots

Solution steps

\int_{0}^{4} 2 x^{2} - 7 x + 3 d x

Eliminate Absolutes

= \int_{0}^{\frac{1}{2}} 2 x^{2} - 7 x + 3 d x + \int_{\frac{1}{2}}^{3} - 2 x^{2} + 7 x - 3 d x + \int_{3}^{4} 2 x^{2} - 7 x + 3 d x

\int_{0}^{\frac{1}{2}} 2 x^{2} - 7 x + 3 d x = \frac{17}{24}

\int_{\frac{1}{2}}^{3} - 2 x^{2} + 7 x - 3 d x = \frac{125}{24}

\int_{3}^{4} 2 x^{2} - 7 x + 3 d x = \frac{19}{6}

= \frac{17}{24} + \frac{125}{24} + \frac{19}{6}

Simplify

\frac{17}{24} + \frac{125}{24} + \frac{19}{6} : \frac{109}{12}

= \frac{109}{12}

(\frac{d y}{d x}) + \frac{2 x y}{x ^{2} + 1} = x

f (x) = - (\frac{1}{3})^{(x + 2)}

n \to 1 lim (\frac{1}{n ^{2}})

\int_{1}^{9} x \cdot ln (x) d x

\int x^{2} + x + 2 d x

What is the integral from 0 to 4 of |2x^2-7x+3| ?
The integral from 0 to 4 of |2x^2-7x+3| is 109/12