Use integration by parts to find the integrals in Exercise.

∫^0_1 ln 3x dx.

0.0986

Step-by-step explanation:

∫^0_1 ln 3x dx

The formula of Integrating by parts is

∫fdg=fg-∫gdf

f=ln (3x), dg=dx

df=1/x dx, g=x

Putting these value in formula

∫fdg=fg-∫gdf=ln (3x) x-∫x*1/xdx=xln (3x) - x=x (ln (3x) - 1) ^0_1

So integration by parts gives

∫ln 3x dx=x (ln (3x) - 1)

Now we solve for given limits

∫^0_1 ln 3x dx=x (ln (3x) - 1) |^0_1=1 (ln (3*1) - 1) = ln3-1=1.0986-1=0.0986

∫^0_1 ln 3x dx=0.0986