What is the integral from 0 to 10 of x^3+x^2+x+1 ?

The integral from 0 to 10 of x^3+x^2+x+1 is 8680/3

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integral from 0 to 10 of x^3+x^2+x+1

\int_{0}^{10} x^{3} + x^{2} + x + 1 d x

\frac{8680}{3}

Decimal

2893.33333 \dots

Solution steps

\int_{0}^{10} x^{3} + x^{2} + 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_{0}^{10} x^{3} d x + \int_{0}^{10} x^{2} d x + \int_{0}^{10} x d x + \int_{0}^{10} 1 d x

\int_{0}^{10} x^{3} d x = 2500

\int_{0}^{10} x^{2} d x = \frac{1000}{3}

\int_{0}^{10} x d x = 50

\int_{0}^{10} 1 d x = 10

= 2500 + \frac{1000}{3} + 50 + 10

Simplify

2500 + \frac{1000}{3} + 50 + 10 : \frac{8680}{3}

= \frac{8680}{3}

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What is the integral from 0 to 10 of x^3+x^2+x+1 ?
The integral from 0 to 10 of x^3+x^2+x+1 is 8680/3