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

The integral from 2 to 3 of (y^2-2y+1) is 7/3

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

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

\frac{7}{3}

Decimal

2.33333 \dots

Solution steps

\int_{2}^{3} y^{2} - 2 y + 1 d y

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{2}^{3} y^{2} d y - \int_{2}^{3} 2 y d y + \int_{2}^{3} 1 d y

\int_{2}^{3} y^{2} d y = \frac{19}{3}

\int_{2}^{3} 2 y d y = 5

\int_{2}^{3} 1 d y = 1

= \frac{19}{3} - 5 + 1

Simplify

\frac{19}{3} - 5 + 1 : \frac{7}{3}

= \frac{7}{3}

What is the integral from 2 to 3 of (y^2-2y+1) ?
The integral from 2 to 3 of (y^2-2y+1) is 7/3