evaluate:∫2dy/(3y-4).. need the solution and answer plz help me to solve this problem,,,tnx,,

Question

anonymous · Answer

why?

zarkon · Answer

$$u=3y-4$$

anonymous · Answer

∫2dy/(3y-4) = 2∫dy/(3y-4)
t = 3y-4 => dt = 3dy => dy = dt/3
2∫dy/(3y-4) = 2∫dt/3t = (2/3)*ln t + C
∫2dy/(3y-4) =[ln (3y-4)^2]/3 + C

amistre64 · Answer

it has to do with reading the future; we need to recognize where 1/(3y-4) comes from derivatively.

ln(3y-4) derives down to 3/(3y-4) times some constant which was pulled out to begin with

amistre64 · Answer

$$\frac{2}{3y-4}=\frac{3}{3y-4}*N$$
$$\frac{2}{3y-4}*\frac{3y-4}{3}=N$$
$$\frac{2}{3}=N$$
$$\frac{2}{3}ln(3y-4)\text{ is at least a reasonable result}$$

amistre64 · Answer

the problems are designed to get you to think "outside" the linear box and get you used to thinking ahead of the problem ...

zarkon · Answer

the absolute value should really be included in the answer unless you write the final solution the way giorgia wrote it.