Area under and between Curves by Integration | ExamSolutions

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When finding an area under a curve to the x-axis we use definite integration. Several types of questions considered. Check out the contents below.
PAGE 1: Area under a curve above the x-axis 0:00:04
PAGE 2:
Example 1 0:01:31
Question 1 - Have a go 0:03:02
PAGE 3: Area below the x-axis 0:06::01
Don't make this common mistake 0:09:13
PAGE 4: Area above and below the x-axis 0:10:55
PAGE 5: Area between a curve and a line 0:14:27
Method 0:15:26
Worked solution 0:17:43
Page 6: Area between two curves 0:21:45
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Videos in this series:
INTEGRATION 1: What is Integration?
A look at basic indefinite integration
• What is Integration? B...
INTEGRATION 2: Definite Integration
Looks at definite integration and applications.
• Definite Integration |...
INTEGRATION 3: Area under a curve
Looks at areas under a curve to the x-axis, below the x-axis, between a curve and a line and between two curves.
• Area under and between...
INTEGRATION 4: Integrals of the form (ax+b)^n
• Integration (ax+b)^n -...
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[@ExamSolutions_Maths]

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[@DaawaaMuslimaHunddaaf]

To be honest mostly I don’t even comment on your videos even though I watched them in a regular basis, because I can’t describe you fully or thank you enough . your explanations are absolutely clear and understandable , also I love the way you organised your works . Thank you so much 😊

[@ExamSolutions_Maths]

That's a nice comment! They do encourage us to continue to make these videos. 👍

[@melysmelys2622]

Yes. This video is by far the easiest and best explanation of finding areas by integration. If I can understand it etc...!

[@vyshakhcp2068]

Hey don't read the comments..just listen to him

[@vyshakhcp2068]

@@abdullahabdulwahab5714 thank me later😌

[@aditiaryal5040]

Hi :) I just wanted to say that your video really helped me! I have an integration test tomorrow and I didn't understand this part of the topic at all, but your video has made me understand what to do and I am very grateful. Thank you!!

[@ExamSolutions_Maths]

Best wishes !

[@arafabdullah4465]

25:21 sir shouldn't it be [-8/3 + 2 + 12] - [-9/8 + 9/8 - 9] which gives 61/3 as a answer and the shaded area will be 397/24. pls do correct me if I am wrong

[@ExamSolutions_Maths]

Hi araf, thank you for your comment. On the second bracket, it seems you accidentally put a negative sign infront of 9/8. That's why you are getting 61/3. Hope this helps. Feel free to ask if anything's confusing. All the best!

[@asogvideos]

Wonderfully done. Hope you could make videos on physics and chemistry as well.

[@soushi3117]

just in time for my mocks tomorrow

[@ExamSolutions_Maths]

Good luck.

[@moqtada5370]

Same 💀

[@tanelkagan]

Question - where there is a curve and a line intersecting, or two curves, then assuming both are "well behaved" across the domain we are looking at (in this case the upper and lower limits of the definite integral) - do we need to integrate once for each function, compute each area, and then subtract areas? Can we not subtract one function from the other and then integrate once? In other words, forgive the notation, but is INT(f1(x))dx - INT(f2(x))dx not INT (f1(x) - f2(x))dx? Can we not basically "pull" the integral out?

[@venkataramsai3226]

Super explanation sir 👌👌👌👌👌👌👌👌👌👌👌👌👌👌👌👌👌👍👌

[@Mr_Blaacck]

Thanks a lot sir. Your explanations are simple but highly effective.

[@claraishungry501]

21:30 i didn't do any of this? i just solved the equations simultaneously to get the x coordinates of points of intersection, then solved the question in like 3 steps. did i do it wrong? (i also got 50/3)

[@MohamadNabilBMNoraziziHiroshim]

Thanks. this help me lot :)

[@uoyebut8953]

I'm getting 8÷3, and you are get 50÷3 for the curve plz clarify for me sir

[@christophermoltisanti2970]

Thanks a lot, this was really helpful.

[@ExamSolutions_Maths]

Glad it was helpful Christopher!

[@danielbradshaw5302]

Very last question, does the area under c² not include all of the are inside the blue curve to where it crosses the x axis, hence is it still included when subtracting the area under c¹ as it is exterior to the two parallel lines. I may be wrong and oblivious but can someone please explain? haha

[@mohammedamanullah9674]

Love from Bangladesh. Thanks for pointing out common mistakes..

[@beatricemulimba8284]

Such brilliance!!! I am Surely going to achieve my goals with such explanation🎉🎉

[@GIFT_AG]

3 years later and this video is still helpful amazing easy to understand explanation thank you sir

[@PatchyPaulina-j7b]

What a life saver,thank you so much this was helpful

[@bernicemarfo2210]

Can you please explain how you had 3 in the first question

[@farhantajwarahmed3340]

How integration gives us area? Like why integration?

[@bongkalo7405]

Farhan Tajwar Ahmed OR Mavi is the best.

[@jimcar53]

superb explanation. Thanks very much.

[@intannajla8342]

good explaination and really helpful, i can prepare for my examination

[@varunnayak5369]

I am trying to prepare for the MAT test ahead of school AS level syllabus so your videos are a lifesaver particularly for the topics which I am unable to understand

[@nethunamaraweera3878]

Thank you very much. This video covered all of the subject matter in igcse edexcel further maths area by integration part. I'm still 15, and if I can figure it out, you all will figure it out. I highly recommend spending this 30 minutes watching this video. 🙏🙌

[@ExamSolutions_Maths]

Well done Nethun! And thanks for recommending us.

[@sanskarbhusal1924]

Very well explained

[@amirandd3658]

This video help me to calculate area under the graph

[@virendrabohara2319]

Love u more 😊💜

[@ExamSolutions_Maths]

:)

[@ymmchaplo9458]

5:00 isnt it supposed to be -1

[@craig7878]

Hi, I was wondering if you could clarify something for me? Given f(x) = x^2-5x+5 and g(x)=-9x+18, I calculated intersection occurs at x = 2 and x = -6. Is that correct to say upper bound is -6 and lower bound is 2? I calculated the area to be -256/3, but i think it should really be positive because area is positive, is that correct?

[@bevamuchie]

Hey, I'm probably late but I believe the lower bound is the smaller number!

[@Reinhard_Erlik]

Lower bound is always the smaller value, for this issue, based on the assumption that all the other processes were unfaulty, you simply need to remove the "-" from the answer and you will have the correct area.

[@assaku]

Thank you so much, this will save me on an exam some day

[@blessedtembo9858]

Wowww thank you!!!!

[@AbdulRehman-dd7kj]

sir can you kindly tell is it mandatory to set y=0 always?

[@mayeeshamusarrat6215]

Yes it is! We're finding the abscissa of the given equation.

[@CharanVelavan]

Thank you Sirrrr so much

[@tinodaisheganyani5729]

Ummm excellent , you are a pure mathematician ..

[@nickolasmasina7747]

thank you very much

[@raisadrawss4190]

super helpful, thank u so much

[@ewanackah3955]

Hi, i really appreciate your videos so thank you for your time. Quick question, I used the limits 4 and -1 and integrated x^2-3x-4 ( I got this by making the the y values = and equating it to 0) and still got the right answer? Was that just luck or can you do it that way? This was for the area between a curve and a line question.

[@khattakjarir3399]

So did i, but i got negative 125/6 lol

[@CharanVelavan]

😍😍😍😍😍😎😎

[@Henry-sp3ku]

thank you mate

[@demindadesilva1418]

This was really helpful

[@nomthandazodube51]

Thanks

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very good video!!!

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[@a.r7688]

Thanks that's great explained really appreciated

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[@ExamSolutions_Maths]

Best wishes

[@stephanietan4437]

Thanxxxxxxx!!!

[@nadeemjabla]

got an exam in two hours and this helped a lot thank youu