Lecture 33: Direct Comparison test for Improper Integrals of Type I and II.

[@user-tw8tj3lw3i]

Thank God I stumbled upon your video. Great explanation Sir! Thank you!

[@DrMathaholic]

Thank you 😊

[@adilkureshi8453]

Excellent💯👍👏

[@engineeringstudent1959]

1.Diverging 2.Diverging 3.Converging

[@DrMathaholic]

Thanks for posting 😊

[@architapatel454]

1) divergent 2) divergent 3) convergent Excellent explaination thank you so much sir

[@DrMathaholic]

Thanks for posting your answer.. Welcome 😀

[@Rajesh_6999]

integral (1-pi/2)tanx/x^3/2

[@DrMathaholic]

Try with this fact-- Tan x> x

[@atta1839]

Thank you sir so much your teaching method is so Best atta from Pakistan

[@DrMathaholic]

Welcome 😊

[@ifranahmed1718]

Thank you sir

[@DrMathaholic]

Thank you 😊👍

[@kputhananangadi]

ty sir

[@DrMathaholic]

Welcome :)

[@leduy5735]

non

[@kartikchavan1317]

At 18:00 answer won't change but shouldn't it be c tending to 0+ HW 1)Diverging 2)Diverging 3)Converging

[@DrMathaholic]

Aah!! Yes.. thanks for careful observation and commenting!! 😊

[@chinmaypande6941]

got the same answers

[@DrMathaholic]

@@chinmaypande6941 great 👍

[@sceptre5240]

what was the g(t) that you took? Because if you take g(t) as 1/t the integral (ln(t)) is not defined at t=0 :(

[@preekshitchandel3981]

Sir ,in question 2 (improper in.of 1st type) we have not chosen g(x) as 1/x^2 as it is not defined(discontinuous)at x=0 ,but in question 3(improper in.of 2nd type) we have opted g(x)=1/sqrtx,but this is also not defined at 0 ,which is in the domain ,can u please clarify this.

[@DrMathaholic]

For 2nd example, f(x) was defined clearly in the complete domain and we need to choose the function g such that it should b continuous then only we can apply the theorem... Whereas for 2nd type, 0 was in the domain and it was problematic point..that's why this integral falls into 2nd point..so we can choose the function where it is not defined at the problematic point.. So for 2nd type it's ok ( choose g such that f and g are not defined at problematic point)...

[@preekshitchandel3981]

Okay ,Thanku so much sir,so can we say for improper integrals of 2nd type we can define g(x) in this way,but for 1st type we need to take care of problematic points??

[@DrMathaholic]

@@preekshitchandel3981 yes...correct..

[@preekshitchandel3981]

@@DrMathaholic okay,thanku so much sir for replying and making the doubt clear.your method of teaching is very unique.

[@DrMathaholic]

@@preekshitchandel3981 welcome and thank you.. Do share with your friends 😊

[@priyankaprabhakar69]

Hello sir how to choose g(x) when function is in terms of log

[@DrMathaholic]

Either ignore log and take watever is left or use the inequality log x less equal x and see what g can be chosen

[@thorrr7613]

In 3rd HW problem , what to take as g(x)???

[@DrMathaholic]

Integrand is even function so write limit from 0 to infinity. Now integrand is e^x/e^2x+1...from here ignore 1 so we get 1/e^x. Now given integrand is less than 1/e^x. So can u try?

[@thorrr7613]

@@DrMathaholic yes sir 😊 , thank you 😊

[@DrMathaholic]

@@thorrr7613 👍👍

[@architapatel454]

Sir i have a question how to solve integration 0 to π/4 (1/√tanx) dx Sir tried to solve but i didn't get the ans

[@DrMathaholic]

Nice question.. Let me think over it..

[@architapatel454]

Okk sir

[@DrMathaholic]

@@architapatel454 answer is converges.. Details I will share later in the evening

[@sanketmourya5136]

Thank you very much sir

[@DrMathaholic]

Welcome :)