What is the integral from 1/2 to 3/2 of x^2+x+1 ?

The integral from 1/2 to 3/2 of x^2+x+1 is 37/12

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integral from 1/2 to 3/2 of x^2+x+1

\int_{\frac{1}{2}}^{\frac{3}{2}} x^{2} + x + 1 d x

\frac{37}{12}

Decimal

3.08333 \dots

Solution steps

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

\int_{\frac{1}{2}}^{\frac{3}{2}} x^{2} d x = \frac{13}{12}

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

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

= \frac{13}{12} + 1 + 1

Simplify

\frac{13}{12} + 1 + 1 : \frac{37}{12}

= \frac{37}{12}

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What is the integral from 1/2 to 3/2 of x^2+x+1 ?
The integral from 1/2 to 3/2 of x^2+x+1 is 37/12