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MRSimplify logarithms😎
@mritunjaylectures
#Integration Basics
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AKFind the missing angles :-
@akhilesh.s.kumar
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MILock in guys 🤓 fix your attention span by watching this entire video 🤭#calculus #tutor #integrals #apcalculus #math
@miracle._.math
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MATwo squares inside a semicircle.
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MATurning points and inflection points often look almost identical on a graph — but mathematically they behave very differently.
At a turning point, the slope becomes zero and the function changes direction.
At an inflection point, the curve changes its shape (concavity), but the function may keep increasing.
Watch the tangents carefully in the animation and see what really changes.
Can you spot the difference?
Save this if it helped you understand calculus more clearly.
@mathwithmudassir
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SUFinding the Volume by revolving the region around the x axis
#definiteintegral #apcalculus
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MRIf o is the centre of circle find out x
@mritunjaylectures
12.0K
PHOne cylinder.
Three integration methods.
Same answer. Why?
Volume of a Cylinder — Three Ways Using Calculus
We know the formula:
V = πr²h
But look deeper — you can derive it in multiple ways.
1️⃣ Using Cylindrical Shells (Radial Integration)
Take a thin cylindrical shell of radius ρ and thickness dρ.
dv = 2πρ × h × dρ
Integrate from 0 to r:
V = ∫₀ʳ 2πρh dρ
= πr²h
2️⃣ Using Angular Sectors (θ Integration)
Take a thin angular slice dθ.
Area of slice = ½ r² dθ
Volume element:
dv = ½ r² h dθ
Integrate from 0 to 2π:
V = ∫₀²π ½ r² h dθ
= πr²h
3️⃣ Using Horizontal Disks (z Integration)
Take thin horizontal slices of thickness dz.
Each slice area = πr²
dv = πr² dz
Integrate from 0 to h:
V = ∫₀ʰ πr² dz
= πr²h
Key Insight 💡
Different coordinate choices.
Different differential elements.
Same physical volume.
That’s the beauty of calculus:
The mathematics changes.
The physics stays consistent.
This is why engineers must understand concepts — not just formulas.
ENGAGEMENT 👇
Which method do you prefer?
A) Radial shells
B) Angular sectors
C) Horizontal disks
Comment your answer.
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AIHow to find common ratio of a GP
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MAPolygon#speed formula#important problem#cbse/icse maths
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AKFind the missing angles :-
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