Question

How do you find the antiderivative of `f(x)=x^6`?

Answer 1

`1/7x^7+c`

Explanation:

Integrate using the `color(blue)"power rule for integration"`

`color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(intax^ndx=a/(n+1)x^(n+1))color(white)(2/2)|)))`

`rArrintx^6dx=1/7x^7+c`

where c is the constant of integration.

Answer 2

`1/7x^7+C`

Explanation:

Antiderivitive means integration:

using the power rule for integration:

`int x^n dx =x^(n+1)/(n+1)+C`

`therefore` `int x^6 dx -> x^7/7+C -> 1/7x^7+C`

This is the final answer:

`1/7x^7+C`