What is the integral from-5 to 2 of (x^2+3x-10) ?

The integral from-5 to 2 of (x^2+3x-10) is -343/6

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integral from-5 to 2 of (x^2+3x-10)

\int_{- 5}^{2} (x^{2} + 3 x - 10) d x

- \frac{343}{6}

Decimal Notation

- 57.16666 \dots

Solution steps

\int_{- 5}^{2} x^{2} + 3 x - 10 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_{- 5}^{2} x^{2} d x + \int_{- 5}^{2} 3 x d x - \int_{- 5}^{2} 10 d x

\int_{- 5}^{2} x^{2} d x = \frac{133}{3}

\int_{- 5}^{2} 3 x d x = - \frac{63}{2}

\int_{- 5}^{2} 10 d x = 70

= \frac{133}{3} - \frac{63}{2} - 70

Simplify

\frac{133}{3} - \frac{63}{2} - 70 : - \frac{343}{6}

= - \frac{343}{6}

\frac{1}{s ^{2} + 4 s + 5}

\int \frac{1}{1 + t ^{2}} d t

- sec (x) + 2 sec^{3} (x)

\frac{x}{x ^{2} + 25}

\frac{d}{d x} (arctan (a x))

What is the integral from-5 to 2 of (x^2+3x-10) ?
The integral from-5 to 2 of (x^2+3x-10) is -343/6