What is the integral from-4 to 3 of x^2+x-12 ?

The integral from-4 to 3 of x^2+x-12 is -343/6

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integral from-4 to 3 of x^2+x-12

\int_{- 4}^{3} x^{2} + x - 12 d x

- \frac{343}{6}

Solution steps

\int_{- 4}^{3} x^{2} + x - 12 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_{- 4}^{3} x^{2} d x + \int_{- 4}^{3} x d x - \int_{- 4}^{3} 12 d x

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

\int_{- 4}^{3} x d x = - \frac{7}{2}

\int_{- 4}^{3} 12 d x = 84

= \frac{91}{3} - \frac{7}{2} - 84

Simplify

\frac{91}{3} - \frac{7}{2} - 84 : - \frac{343}{6}

= - \frac{343}{6}

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

\int_{0}^{1} (x^{3} - x + 1) d x

\int_{0}^{1} \frac{x - x}{2} d x

\int_{0}^{3} r d r

\int_{0}^{1} \frac{x}{y} d x

What is the integral from-4 to 3 of x^2+x-12 ?
The integral from-4 to 3 of x^2+x-12 is -343/6