Question

evaluate the integral using the Fundamental Theorem of Calculus (i.e. antiderivatives) to
determine the exact value:
integral of (10)/(3x+1) from 0 to 3

Answer 1

\[\int\limits_{0}^{3}\frac{ 10 }{ 3x+1 } *dx\]

Answer 2

\[10*\int\limits_{0}^{3}\frac{ dx }{ 3x+1 }\]

Answer 3

as 10 is constant u can take it out

Answer 4

let
3x+1=u
so new limit will be
for x=0
u=3*0+1=1
for x=3
u=3*3+1=10
from 1 to 10
now 3x+1=u
differntiate
3*dx=du
dx=du/3

Answer 5

so now nem integral is
\[10*\int\limits_{1}^{10}\frac{ du }{ 3 *u }\
]take 1/3 out
\[\frac{ 10 }{ 3 }* \int\limits_{1}^{10} \frac{ du }{ u }\]

Answer 6

du/u=Ln(u) ln= natural log

Answer 7

hello @gorv ! so are your writing all of this out it is all coming back to me!! :)

Answer 8

\[\frac{ 10 }{ 3 }\left[ \ln u \right]\]
with limi from 1 to 10

Answer 9

yay i got that as well :)

Answer 10

what ????

Answer 11

First approaching the problem i couldn't think of how to solve. but as you were explaining, i was able to remember how do to it. but i very much appreciate your help!

Answer 12

ohhhh i thought somthin else lolll