What is the integral from-3 to 4 of (x^2+3x+1) ?

The integral from-3 to 4 of (x^2+3x+1) is 287/6

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integral from-3 to 4 of (x^2+3x+1)

\int_{- 3}^{4} (x^{2} + 3 x + 1) d x

\frac{287}{6}

Decimal

47.83333 \dots

Solution steps

\int_{- 3}^{4} x^{2} + 3 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_{- 3}^{4} x^{2} d x + \int_{- 3}^{4} 3 x d x + \int_{- 3}^{4} 1 d x

\int_{- 3}^{4} x^{2} d x = \frac{91}{3}

\int_{- 3}^{4} 3 x d x = \frac{21}{2}

\int_{- 3}^{4} 1 d x = 7

= \frac{91}{3} + \frac{21}{2} + 7

Simplify

\frac{91}{3} + \frac{21}{2} + 7 : \frac{287}{6}

= \frac{287}{6}

What is the integral from-3 to 4 of (x^2+3x+1) ?
The integral from-3 to 4 of (x^2+3x+1) is 287/6