What is the integral from 0 to 1 of (x^4)^2-(x^7)^2 ?

The integral from 0 to 1 of (x^4)^2-(x^7)^2 is 2/45

Popular >

integral from 0 to 1 of (x^4)^2-(x^7)^2

\int_{0}^{1} (x^{4})^{2} - (x^{7})^{2} d x

\frac{2}{45}

Decimal Notation

0.04444 \dots

Solution steps

\int_{0}^{1} (x^{4})^{2} - (x^{7})^{2} d x

Simplify

(x^{4})^{2} - (x^{7})^{2} : x^{8} - x^{14}

= \int_{0}^{1} x^{8} - x^{14} 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_{0}^{1} x^{8} d x - \int_{0}^{1} x^{14} d x

\int_{0}^{1} x^{8} d x = \frac{1}{9}

\int_{0}^{1} x^{14} d x = \frac{1}{15}

= \frac{1}{9} - \frac{1}{15}

Simplify

\frac{1}{9} - \frac{1}{15} : \frac{2}{45}

= \frac{2}{45}

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

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

\int_{0}^{π} 5 sin (t) d t

\int_{l n (4)}^{l n (5)} e^{x} d x

\int_{2}^{7} 9 x^{2} d x

What is the integral from 0 to 1 of (x^4)^2-(x^7)^2 ?
The integral from 0 to 1 of (x^4)^2-(x^7)^2 is 2/45