Question

How do you compute the value of `int x^5 dx` of `[1,2]`?

Answer 1

`int_1^2 x^5dx = 21/2`

Explanation:

Using the power rule for integration; `int x^n=x^(n+1)/(n+1) (+c)`

We have:
`int_1^2 x^5dx = [x^6/6]_1^2`

`:. int_1^2 x^5dx = 1/6 [x^6]_1^2`

`:. int_1^2 x^5dx = 1/6 { 2^6 - 1^6 }`
`:. int_1^2 x^5dx = 1/6 { 64- 1 }`
`:. int_1^2 x^5dx = 63/6`
`:. int_1^2 x^5dx = 21/2`