What is the integral from 2 to 3 of (7x^2+5x+4) ?

The integral from 2 to 3 of (7x^2+5x+4) is 365/6

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integral from 2 to 3 of (7x^2+5x+4)

\int_{2}^{3} (7 x^{2} + 5 x + 4) d x

\frac{365}{6}

Decimal

60.83333 \dots

Solution steps

\int_{2}^{3} 7 x^{2} + 5 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_{2}^{3} 7 x^{2} d x + \int_{2}^{3} 5 x d x + \int_{2}^{3} 4 d x

\int_{2}^{3} 7 x^{2} d x = \frac{133}{3}

\int_{2}^{3} 5 x d x = \frac{25}{2}

\int_{2}^{3} 4 d x = 4

= \frac{133}{3} + \frac{25}{2} + 4

Simplify

\frac{133}{3} + \frac{25}{2} + 4 : \frac{365}{6}

= \frac{365}{6}

What is the integral from 2 to 3 of (7x^2+5x+4) ?
The integral from 2 to 3 of (7x^2+5x+4) is 365/6