15.2: Double Integrals over General Regions

Objectives:
2. Evaluate an iterated integral by reversing the order of operation.
3. Find the volume of certain solids using an iterated integral in rectangular coordinates.

[@user-rm9oi2jd8r]

My school cancelled all face to face classes for the rest of the semester. Your videos help me continue studying the course material. Many thanks.

[@user-dx3qg4tn6g]

me 2

[@Lostwolf16]

After 3 hours of hopeless attempts this video saved me. Thank you for making it intuitive rather than telling us to memorize The way you look at it is 100 times better than Type 1 and Type 2

[@rigelmax7624]

I really appreciate people that go over these concepts while following the text book. thx

[@audreymukhari1248]

I've never understood calculus this clearly. . .Blessings. . Work appreciated. Gifted.

[@Jessica_Le]

Amazing teacher! I love how you explained everything clearly and always made sure your students catch up. Please keep posting!

[@dr.mohamedaitnouh4501]

Thank you Professor Niedden it helps me a lot since I am teaching on the same textbook ... again thank you!

[@prathameshagrawal5244]

Awsm video , very concise and to the point , thank you for providing such quality material

[@captionato]

thanks so much btw. this is helping me when my lecturers cant explain in online classes. this saved me from stress.

[@earthtotracee]

Hi! thank you so much for posting this! im a student at University of Washington and found this to be so helpful!!

[@kanishka5957]

Crystal clear lecture ♥️

[@aleikac2352]

thank you so much for sharing this video and explaining so clearly.

[@stephanbotes5865]

I think each of the videos has a "Bless you," moment. Hehehehe

[@shivamverma2754]

eggzackly ma'am is just awesome :))

[@z1designs828]

You are carrying me through calc 4 !!

[@ep8587]

omg I love you this is so clear to understand my prof sucks

[@LucasCosta-wh5xk]

could you explain how you got the points (5,4) and (-1,-2) ? thank you! love your vids

[@alexandraniedden5337]

The points (5.4) and (-1,-2) are the intersection points of the two graphs. Because the two equations are y=x-1 and y^2=2x+6, I set (x-1)^2 = 2x+6 (both sides = y^2). You'll end up squaring the left side and moving everything to one side to get x^2 - 4x - 5 = 0. Factoring you find x = 5, -1. Substitute these into either equation to find the corresponding y-values. You will then use these two points to set up your limits of integration. Hope this helps!

[@twipps7700]

This helped me a ton thank you

[@spivak4342]

Thank you sincerely

[@stephanbotes5865]

Math made easy. Thank you!

[@iced751]

Also at 35:04, the antiderivative of y is y^2/2 correct? So shouldn't it be y^2/2 then you'd have -1/2y^2 * -cos

[@richardyt2755]

Great Great Tutorial!

[@petersun3454]

what do you mean always constant? How do you decide what to integrate first?

[@user-jk2kr9in2f]

Thank you so much ...

[@moisesdevs]

Not all heroes wear capes.

[@Bearisgoodboy28]

came here after reading the text book, helped a bunch

[@juanmanuelmillansanchez8165]

You sound pissed off 😤, but I really appreciated your video. Thank u!!!!

[@tonatiuhdeleon8236]

yeah haha

[@ZeroTwo00002]

so cleeean! ty

[@rashwanmohamed4545]

Thanks alot

[@jayanthkousthubhaeswarmyla6419]

How will get that y+1 > y²/2 - 3

[@mangcobo_blackrose]

You've got a smart class right there however, some of us do want to know why you opted to integrate with x first

[@alexandraniedden5337]

Can you give me a time stamp? I'm not sure which example you are referring to.

[@mangcobo_blackrose]

Ex#3 around 18 min.

[@alexandraniedden5337]

@@mangcobo_blackrose I chose to integrate with respect to x first because there are consistent left and right bounds (the left bound is the parabola and the right bound is the line). If I were to integrate with respect to y first, that would be more difficult because the bottom bound changes. The top bound is always the parabola. The bottom bound is the parabola from x = -3 to x = -1, then the bottom bound becomes the line from x = -1 to x = 5. This would require two double integrals to calculate the same volume.

[@mangcobo_blackrose]

@@alexandraniedden5337 Thank you very much👏👏🙌

[@danielasepulveda9143]

Thank you

[@SamSam-yy8sd]

Wonderful great nice thank u ,god bless u

[@cringingyukino3282]

Still can't figure out how to set the bounds of the inner integral

[@justinwesley7041]

how to find the limit of x?...you not mention it

[@algorithmo134]

is there topics on real analysis?

[@angelagorman6981]

Answer to Example 5 if you please. Thanks.

[@vxcute0]

Thank you my exam is after 5 days.

[@mokgethoasehorane4735]

Dankoo is thank you

[@alexgao5543]

nice

[@Exploringpakistanbeauty]

❤️❤️❤️❤️

[@m4lgam]

this video is fucking bomb thank you

[@9LimaAlpha7]

you need to go into the specifics 24:23

[@9LimaAlpha7]

why arnt you explaing the solutions??? 28:28

[@sweetpandaplays5326]

at 10:51 sec.... u have calculated wrong....... it should be -4x^2 - x^3 + x^2 +x +1

[@knanzeynalov7133]

Good content but you did not specifically explain how to find bounds and sketch the graph.

[@benjaminandrew7940]

30:11 I got 39?? Before I commented this I looked at yours and realised that I had not distributed the 1/2 to the +1 in the first paranthesis. if anyone else did that I will still comment

[@freeguylota]

She really gave us the two minutes!😂

[@ayushmisra2226]

my stevens institute of tech prof used the exact same notes and examples lol\

[@harithamsyar5689]

answers for eample 2???

[@alexandraniedden5337]

0!

[@harithamsyar5689]

@@alexandraniedden5337 Thanks for replying miss glad that I get the same...greetings from Malaysia :)

[@gunavardhansaiputta3483]

How can area be 0!

[@hassenabubeker7312]

i was confused with the minor mistake you made at first then you corrected it

[@mivuyompateni9075]

as in like the first example?

[@majdybrown9470]

idk why but i smell pancake while watching this video

[@princekaodi3868]

but improve your voice plz

[@blessedtanakanobela5323]

Great content........ i suggest you cut your videos and put different title on KZbin for example . Double boundary concepts and the other one examples . People aren’t you to watch long videos