# Tutor.com The Definite Integral Session

##### Mar. 15, 2012

Session Transcript - Math - Calculus, 3/8/2012 11:30PM - Tutor.comSession Date: 3/8/2012 11:30PM
Length: 21.2 minute(s)
Subject: Math - Calculus

System Message
[00:00:00] *** Please note: All sessions are recorded for quality control. ***

Tiffany (Customer)
[00:00:00] help with problem

Gilberto E (Tutor)
[00:00:11] Hi

Tiffany (Customer)
[00:00:23] i need help evaluating an integral using the fumdemental theorem

Gilberto E (Tutor)
[00:00:37] Ok. Let's see it

Tiffany (Customer)
[00:02:13] that's it

Gilberto E (Tutor)
[00:02:31] Ok. How have you tried to approach this problem ?

Tiffany (Customer)
[00:03:34] I have no clue how to solve it.

Gilberto E (Tutor)
[00:03:56] That's ok. One sec..
[00:04:59] Ok. How about we try a u substitution?

Tiffany (Customer)
[00:05:16] ok

Gilberto E (Tutor)
[00:05:39] what will be du?

Tiffany (Customer)
[00:06:36] i am not sure

Gilberto E (Tutor)
[00:07:06] What's the derivative of secx?

Tiffany (Customer)
[00:07:30] secxtanx

Gilberto E (Tutor)
[00:07:45] Good
[00:08:34] and what will be our new bounds?

Tiffany (Customer)
[00:09:16] i am not sure

Gilberto E (Tutor)
[00:09:36] Do you know how to solve for the new bounds ?

Tiffany (Customer)
[00:10:27] no.

Gilberto E (Tutor)
[00:10:43] That's ok. You will learn today
[00:11:04] Simply, let's plug each of our bounds into secx to get them in terms of u.
[00:11:34] what is sec(pi/3)?

Tiffany (Customer)
[00:12:41] 2

Gilberto E (Tutor)
[00:12:48] Good
[00:12:55] and sec(0)?

Tiffany (Customer)
[00:13:13] 0

Gilberto E (Tutor)
[00:13:25] Are you sure?

Tiffany (Customer)
[00:13:44] 1

Gilberto E (Tutor)
[00:13:50] Good
[00:14:09] Ok. So we got everything set. Now what's next?

Tiffany (Customer)
[00:14:48] not sure

Gilberto E (Tutor)
[00:15:05] Well, what's the integral of 4?

Tiffany (Customer)
[00:15:33] 4x

Gilberto E (Tutor)
[00:15:42] 4u
[00:15:59] what's next?

Tiffany (Customer)
[00:16:53] do we substitute 2 for u

Gilberto E (Tutor)
[00:17:02] yes

Tiffany (Customer)
[00:18:14] 8-4 = 4 ?

Gilberto E (Tutor)
[00:18:26] Awesome!

Tiffany (Customer)
[00:19:04] is that the final answer?

Gilberto E (Tutor)
[00:19:13] Yes

Tiffany (Customer)
[00:19:23] can you explain again how we set up the new bounds?

Gilberto E (Tutor)
[00:19:32] Sure.
[00:19:50] We simply take our original bounds, and plug them in for whatever we let u equal.
[00:20:30] whatever the answers are, we choose as our bounds

Tiffany (Customer)
[00:20:54] ok
[00:20:57] thank you

Gilberto E (Tutor)
[00:21:01]
[00:21:05] No problem.
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