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

The integral from 1 to 2 of (x^2+3x^4) is 314/15

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

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

\frac{314}{15}

Decimal Notation

20.93333 \dots

Solution steps

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

\int_{1}^{2} x^{2} d x = \frac{7}{3}

\int_{1}^{2} 3 x^{4} d x = \frac{93}{5}

= \frac{7}{3} + \frac{93}{5}

Simplify

\frac{7}{3} + \frac{93}{5} : \frac{314}{15}

= \frac{314}{15}

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(1.1) (3.4)

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

What is the integral from 1 to 2 of (x^2+3x^4) ?
The integral from 1 to 2 of (x^2+3x^4) is 314/15