Question

How do you find the definite integral for: `((x^(6))dx` for the intervals `[b, 2b]`?

Answer 1

`127/7 b^7`

Explanation:

`int_b^(2b)x^6dx=[1/7x^7]_b^(2b)`

Note that this antiderivative was obtained using the rule `int_a^bx^ndx=[1/(n+1)x^(n+1)]_a^b`.

`=1/7[(2b)^7-b^7]=1/7(128b^7-b^7)=1/7(127b^7)`

`rArrint_b^(2b)x^6dx=127/7 b^7`