What is the integral from 5 to 7 of x^2+x+1-15 ?

The integral from 5 to 7 of x^2+x+1-15 is 170/3

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integral from 5 to 7 of x^2+x+1-15

\int_{5}^{7} x^{2} + x + 1 - 15 d x

\frac{170}{3}

Decimal

56.66666 \dots

Solution steps

\int_{5}^{7} x^{2} + x + 1 - 15 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}^{7} x^{2} d x + \int_{5}^{7} x d x + \int_{5}^{7} 1 d x - \int_{5}^{7} 15 d x

\int_{5}^{7} x^{2} d x = \frac{218}{3}

\int_{5}^{7} x d x = 12

\int_{5}^{7} 1 d x = 2

\int_{5}^{7} 15 d x = 30

= \frac{218}{3} + 12 + 2 - 30

Simplify

\frac{218}{3} + 12 + 2 - 30 : \frac{170}{3}

= \frac{170}{3}

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\int_{0}^{1} (2 x e^{x^{2}}) d x

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What is the integral from 5 to 7 of x^2+x+1-15 ?
The integral from 5 to 7 of x^2+x+1-15 is 170/3