Theodore K.
asked • 09/08/14integrate using "reversed" substitution
Using the substitution x=(√3)tany find the exact value of
1∫3 1/√(3+x^2) dx
expressing your answer as a single logarithm in terms of y
1∫3 1/√(3+x^2) dx
expressing your answer as a single logarithm in terms of y
More
1 Expert Answer
SURENDRA K. answered • 09/08/14
Tutor
New to Wyzant
An experienced,patient & hardworking tutor
x= sqrt(3)tan(t)
dx=sqrt(3)sec(t)^2dt
Integrand after substitution
=sqrt(3)sec(t)^2dt/sqrt(3)sec(t)
=sec(t)dt
After integration
=ln|sec(t)+tan(t)|
=ln|sqrt((x^2+3)/3)+x/sqrt(3)|
now take limits from 1-3
ln|2+sqrt(3)|-ln|sqrt(3)
any questions,welcome
Theodore K.
how did 1/√(3+x^2) dx become √(3)sec2(t) / √(3)sec(t)
also the limits should be changed to fit the substitution 1 becomes pi/6 and 3 becomes pi/3
Report
09/09/14
SURENDRA K.
x= sqrt(3)tan(t)
dx=sqrt(3)sec(t)^2dt
dx/sqrt(3+x^2)=sqrt(3)sec(t)^2dt/sqrt(3)sec(t)
= sec(t)dt
You change the limits from pi/6 to pi/3,work it out and you shall get the same answer.
What I have done is substitute back after integration and limits from 1-3.It amounts the same.
Hope that helps you.
Report
09/09/14
Still looking for help? Get the right answer, fast.
Ask a question for free
Get a free answer to a quick problem.
Most questions answered within 4 hours.
OR
Find an Online Tutor Now
Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.
Emma D.
09/17/14