Question

How do you evaluate the definite integral `int (14x^6)dx` from [-2,2]?

Answer 1

`512`

Explanation:

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)|)))`

`rArrint_-2^2(14x^6)dx=14/7[x^7]_-2^2`

`=2[x^7]_-2^2`

Evaluate the upper and lower limits and subtract upper - lower

`=2[(2^7)-(-2)^7)]=2(128-(-128))=512`