# Tutor.com The Definite Integral Session

##### Mar. 14, 2014

Session Transcript - Math - Calculus, 1/20/2014 5:03PM - Tutor.comSession Date: 1/20/2014 5:03PM
Length: 25.4 minute(s)
Subject: Math - Calculus

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Guest (Customer)
[00:00:00] hi

Daniel C (Tutor)
[00:00:58] Hello. Welcome to Tutor.com !

Guest (Customer)
[00:01:09] ill post it on the board! :)

Daniel C (Tutor)
[00:01:13] Thanks

Guest (Customer)
[00:01:35] thats 4t+5^2.2

Daniel C (Tutor)
[00:01:45] okay.. good.. got it...
[00:01:50] How do you think we should start this problem?

Guest (Customer)
[00:03:12] we just need the anti derivative right

Daniel C (Tutor)
[00:04:01] Yes!... but we may use a particular strategy to find it.. for example, are you familiar with u-substituition?

Guest (Customer)
[00:04:50] kinda
[00:04:57] haven't practiced it yet

Daniel C (Tutor)
[00:05:09] okay.. this is the moment
[00:05:11] :D
[00:05:25] let's use u = 4 l +5
[00:06:03] what is the derivative of 4l+5?
[00:07:27] Do you understand how we did that last part?

Guest (Customer)
[00:07:44] yup!

Daniel C (Tutor)
[00:08:17] oh
[00:08:19] thanks

Guest (Customer)
[00:09:06] this is the part where i get confused

Daniel C (Tutor)
[00:09:20] okay.. no worries.. let's do it together...

Guest (Customer)
[00:09:32] ohhh ok
[00:09:35] i see that

Daniel C (Tutor)
[00:09:50] What would we get?
[00:10:53] Do you need a hand?

Guest (Customer)
[00:11:02] what would we get for what?

Daniel C (Tutor)
[00:11:13] making the substitution

Guest (Customer)
[00:12:09] where did the 1/4 come from
[00:12:15] thats the step that confuses me

Daniel C (Tutor)
[00:12:27] okay.. let's go back a little bit
[00:12:38] we have du = 4 dt.. is that clear so far?

Guest (Customer)
[00:12:55] yup

Daniel C (Tutor)
[00:13:24] okay.. now we solve for dt
[00:13:59] is that step clear?

Guest (Customer)
[00:14:10] ohhhhhh ok
[00:14:44] now we subsitutd the integral
[00:14:49] in terms of u

Daniel C (Tutor)
[00:14:50] Exactly!
[00:14:54] Sweet!

Guest (Customer)
[00:14:53] u^2.2

Daniel C (Tutor)
[00:15:02] Awesome!

Guest (Customer)
[00:15:01] *1/4du

Daniel C (Tutor)
[00:15:05] Exactly!
[00:15:37] Do you understand how we did that last part?

Guest (Customer)
[00:15:46] yup!!

Daniel C (Tutor)
[00:15:50] Good!
[00:16:20] What should we do next?

Guest (Customer)
[00:16:31] anti deriv
[00:16:35] so u^3.2/3.2
[00:16:45] ?

Daniel C (Tutor)
[00:16:57] Cool!

Guest (Customer)
[00:17:20] I have a question, after you have u, du, and dt

Daniel C (Tutor)
[00:17:25] and what is u?
[00:17:28] oh.. tell me

Guest (Customer)
[00:17:46] then, can you substitute the integral?
[00:18:01] i guessm question is just about the steps, for solving any integral
[00:18:08] must find, u, du and dt
[00:18:17] then substitute that in the original integral?

Daniel C (Tutor)
[00:18:41] Exactly.. so we can have the integral in terms of u
[00:18:43] ;)

Guest (Customer)
[00:18:49] ok cool
[00:18:54] now we can proceed
[00:19:02] what happen to the du?

Daniel C (Tutor)
[00:19:29] when we applied the antiderivative rule, it dissapeared

Guest (Customer)
[00:19:43] ok

Daniel C (Tutor)
[00:19:50] the integral symbol is also gone

Guest (Customer)
[00:19:53] and why does the 1/4 go on the outside?

Daniel C (Tutor)
[00:20:15] oh.. that is a property of the integrals...
[00:20:42] we can take a constant out of an integral
[00:20:55] do you see where it comes from?

Guest (Customer)
[00:21:32] yup!
[00:21:43] now we can put u back in

Daniel C (Tutor)
[00:21:53] Exactly!

Guest (Customer)
[00:22:25] 4t+5

Daniel C (Tutor)
[00:22:29] Cool!
[00:22:44] Does this problem make sense to you now?Â

Guest (Customer)
[00:23:01] yup!
[00:23:10] let me try submitting that first

Daniel C (Tutor)
[00:23:27] okay

Guest (Customer)
[00:24:16] alright cool!
[00:24:21] its A-ok!

Daniel C (Tutor)
[00:24:22] :D
[00:24:26] Sweet!

Guest (Customer)
[00:24:37] thanks!

Daniel C (Tutor)
[00:24:44] You're welcome!

Guest (Customer)
[00:24:48] time to log back on for my other questions.. they get more diffucult

Daniel C (Tutor)
[00:24:49] It was nice working with you!

Guest (Customer)
[00:24:54] but still using u sub

Daniel C (Tutor)
[00:25:06] Good luck!

Guest (Customer)
[00:25:06] great!
[00:25:07] thanks
[00:25:08] :)

Daniel C (Tutor)
[00:25:11] And thanks for using our services!

Guest (Customer)
[00:25:11] have a good day

Daniel C (Tutor)
[00:25:16] You too!
[00:25:19] Good bye!

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