What is the integral from 0 to 1 of 7x^6(6-x^7) ?

The integral from 0 to 1 of 7x^6(6-x^7) is 11/2

Popular >

integral from 0 to 1 of 7x^6(6-x^7)

\int_{0}^{1} 7 x^{6} (6 - x^{7}) d x

\frac{11}{2}

Decimal

5.5

Solution steps

\int_{0}^{1} 7 x^{6} (6 - x^{7}) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 7 \cdot \int_{0}^{1} x^{6} (6 - x^{7}) d x

Expand

x^{6} (6 - x^{7}) : 6 x^{6} - x^{13}

= 7 \cdot \int_{0}^{1} 6 x^{6} - x^{13} 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

= 7 (\int_{0}^{1} 6 x^{6} d x - \int_{0}^{1} x^{13} d x)

\int_{0}^{1} 6 x^{6} d x = \frac{6}{7}

\int_{0}^{1} x^{13} d x = \frac{1}{14}

= 7 (\frac{6}{7} - \frac{1}{14})

Simplify

7 (\frac{6}{7} - \frac{1}{14}) : \frac{11}{2}

= \frac{11}{2}

\int_{1}^{\frac{8}{5}} \frac{1}{x ^{2}} d x

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

\int_{- 2}^{1} [(2 - y) - y^{2}] d y

\int_{0}^{2} (4 - x^{2})^{3} d x

\int_{- 2}^{0} \frac{1}{1 - 4 x} d x

What is the integral from 0 to 1 of 7x^6(6-x^7) ?
The integral from 0 to 1 of 7x^6(6-x^7) is 11/2