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ITFundamental theorem of calculus!
#calculus #math #integral #finals #ap
@itzz_jorawar001
#Integrate Cotx
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CAdo you have your half angle identities memorized? #calculus #mathematics #math #maths #education
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ELFundamental Theorem of Calculus (Part 1) in action.
When a function is defined as an integral with a variable upper limit, we don’t integrate again — we differentiate, and the theorem does the heavy lifting.
#math #calculus #derivatives #integration
@electricalmath
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CAyou really can’t do a trig integral problem without a typo, right?? 😬 #calculus #mathematics #math #maths #education
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DRU-substitution Calculus Practice Problem explained
#calculus #integral #calctutor
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ELLet’s solve this seemingly challenging integral involving a logarithm and trigonometric functions of different angles.
A clever solution involving three substitutions!
#math #calculus #integration #integrals
@electricalmath
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DAThe Most Beautiful Equation in Calculus
This function is its own derivative AND its own integral. Mind = blown.
The only shape of function that does this.
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#math #calculus #mathisfun #learnontiktok #edutok #stem #mathematics #derivative #integral #euler #mathtok #school #learning #satisfying
@dailymathvisuals
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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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ELLet’s integrate this rational function in 1 minute.
The standard approach is to factorise the denominator and use partial fraction decomposition, which is not too bad. But factoring out the highest power of x instead of the lowest one actually leads to a clever substitution that simplifies the solution a great deal.
Some food for thought: What characteristic of the polynomial in the denominator makes this substitution work? Can you generalize this?
#math #calculus #integration #integral
@electricalmath
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LECalculus #integration
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