What is the integral from 3 to 5 of x^2+2x-6 ?

The integral from 3 to 5 of x^2+2x-6 is 110/3

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integral from 3 to 5 of x^2+2x-6

\int_{3}^{5} x^{2} + 2 x - 6 d x

\frac{110}{3}

Decimal Notation

36.66666 \dots

Solution steps

\int_{3}^{5} x^{2} + 2 x - 6 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}^{5} x^{2} d x + \int_{3}^{5} 2 x d x - \int_{3}^{5} 6 d x

\int_{3}^{5} x^{2} d x = \frac{98}{3}

\int_{3}^{5} 2 x d x = 16

\int_{3}^{5} 6 d x = 12

= \frac{98}{3} + 16 - 12

Simplify

\frac{98}{3} + 16 - 12 : \frac{110}{3}

= \frac{110}{3}

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What is the integral from 3 to 5 of x^2+2x-6 ?
The integral from 3 to 5 of x^2+2x-6 is 110/3