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

1 Answer
Sep 15, 2016

int_0^1 8/(3+4x)dx=2ln(7/3), or, =ln(49/9).

Explanation:

We know that, int1/tdt=ln|t|+C...........(1)

If we let, t=3+4x, "then", dt=4dx.

By (1), "then", int1/(3+4x)*4dx=ln|3+4x|+C, or,

int 8/(3+4x)dx=2ln|3+4x|+C.

Therefore,

int_0^1 8/(3+4x)dx=2[ln|3+4x|]_0^1

=2[ln7-ln3]=2ln(7/3)

:. int_0^1 8/(3+4x)dx=2ln(7/3), or, =ln(49/9).

Enjoy Mats.!