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
INTEGRATION 2: Definite Integration
Looks at definite integration and applications.
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.
INTEGRATION 4: Integrals of the form (ax+b)^n
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DaawaaMuslimaHunddaaf

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Thank you!!

aditiaryal

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amirandd

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christophermoltisanti

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tinodaisheganyani

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?

tanelkagan

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

nadeemjabla

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

arafabdullah

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