What is the integral from 0 to 1 of x^2-3x+5 ?

The integral from 0 to 1 of x^2-3x+5 is 23/6

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integral from 0 to 1 of x^2-3x+5

\int_{0}^{1} x^{2} - 3 x + 5 d x

\frac{23}{6}

Decimal

3.83333 \dots

Solution steps

\int_{0}^{1} x^{2} - 3 x + 5 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}^{1} x^{2} d x - \int_{0}^{1} 3 x d x + \int_{0}^{1} 5 d x

\int_{0}^{1} x^{2} d x = \frac{1}{3}

\int_{0}^{1} 3 x d x = \frac{3}{2}

\int_{0}^{1} 5 d x = 5

= \frac{1}{3} - \frac{3}{2} + 5

Simplify

\frac{1}{3} - \frac{3}{2} + 5 : \frac{23}{6}

= \frac{23}{6}

\int_{0}^{1} x^{2} - 3 x + 6 d x

\int_{0}^{2 x} e^{- x^{2}} d x

\int_{\frac{π}{3}}^{\frac{π}{2}} x + cos (x) d x

\int_{1}^{2} \frac{x ^{2} - 12}{x ^{4}} d x

\int_{3}^{6} (3 x^{2} + x - 3) d x

What is the integral from 0 to 1 of x^2-3x+5 ?
The integral from 0 to 1 of x^2-3x+5 is 23/6