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

The integral from-1 to 2 of x(1+x^3) is 81/10

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

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

\frac{81}{10}

Decimal Notation

8.1

Solution steps

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

Expand

x (1 + x^{3}) : x + x^{4}

= \int_{- 1}^{2} x + 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 d x + \int_{- 1}^{2} x^{4} d x

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

\int_{- 1}^{2} x^{4} d x = \frac{33}{5}

= \frac{3}{2} + \frac{33}{5}

Simplify

\frac{3}{2} + \frac{33}{5} : \frac{81}{10}

= \frac{81}{10}

\frac{d}{d x} (\frac{1}{10} (x - 60)^{2} + 100)

- 7 x^{2}

sin^{2} (x)

\int \frac{1}{sec ^{2} ( θ )} d θ

What is the integral from-1 to 2 of x(1+x^3) ?
The integral from-1 to 2 of x(1+x^3) is 81/10