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

The integral from 3 to 4 of (x+7x^2) is 539/6

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

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

\frac{539}{6}

Decimal

89.83333 \dots

Solution steps

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

\int_{3}^{4} x d x = \frac{7}{2}

\int_{3}^{4} 7 x^{2} d x = \frac{259}{3}

= \frac{7}{2} + \frac{259}{3}

Simplify

\frac{7}{2} + \frac{259}{3} : \frac{539}{6}

= \frac{539}{6}

What is the integral from 3 to 4 of (x+7x^2) ?
The integral from 3 to 4 of (x+7x^2) is 539/6