What is the integral from 1 to 3 of 2x^2+2x+4 ?

The integral from 1 to 3 of 2x^2+2x+4 is 100/3

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integral from 1 to 3 of 2x^2+2x+4

\int_{1}^{3} 2 x^{2} + 2 x + 4 d x

\frac{100}{3}

Decimal

33.33333 \dots

Solution steps

\int_{1}^{3} 2 x^{2} + 2 x + 4 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_{1}^{3} 2 x^{2} d x + \int_{1}^{3} 2 x d x + \int_{1}^{3} 4 d x

\int_{1}^{3} 2 x^{2} d x = \frac{52}{3}

\int_{1}^{3} 2 x d x = 8

\int_{1}^{3} 4 d x = 8

= \frac{52}{3} + 8 + 8

Simplify

\frac{52}{3} + 8 + 8 : \frac{100}{3}

= \frac{100}{3}

What is the integral from 1 to 3 of 2x^2+2x+4 ?
The integral from 1 to 3 of 2x^2+2x+4 is 100/3