What is the integral from 1 to 3 of (2x^2-2x+3) ?

The integral from 1 to 3 of (2x^2-2x+3) is 46/3

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integral from 1 to 3 of (2x^2-2x+3)

\int_{1}^{3} (2 x^{2} - 2 x + 3) d x

\frac{46}{3}

Decimal Notation

15.33333 \dots

Solution steps

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

\int_{1}^{3} 2 x^{2} d x = \frac{52}{3}

\int_{1}^{3} 2 x d x = 8

\int_{1}^{3} 3 d x = 6

= \frac{52}{3} - 8 + 6

Simplify

\frac{52}{3} - 8 + 6 : \frac{46}{3}

= \frac{46}{3}

\int sin (\frac{nπ x}{l}) d x

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

\int e^{- y^{2}} d y

y = \frac{2}{x}, (- 3, - \frac{2}{3})

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

What is the integral from 1 to 3 of (2x^2-2x+3) ?
The integral from 1 to 3 of (2x^2-2x+3) is 46/3