Question

How do you evaluate the definite integral `int (8)/sqrt(3+4x)` from `[0,1]`?

Answer 1

definite integral `=4(sqrt7-sqrt3)`

Explanation:

Use the substitution `u=3+4x`
Then `du/dx=4`
`dx=(du)/4`
So the integral is `int(8dx)/(sqrt(3+4x))=int(2du)/sqrtu=2*sqrtu/(1/2)=4sqrtu`
going back to x
`int_0^1(8dx)/(sqrt(3+4x))=4sqrt(3+4x)∣_0^1=4sqrt7-4sqrt3`