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ONI’ll never switch up on my formula
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#integration #integrationbyparts #math #mathjoke #calculus
@onetaptutoring
#Intergration
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MASummation and integration are both ways of adding quantities together, but they are used in different mathematical situations. A summation is used when we add a set of separate, countable values. For example, if we want to add the values of a sequence or combine several measurements, we use a sum. Each value is clearly distinct and added one after another. Because of this, summation is commonly used in discrete mathematics, sequences, statistics, and situations where data appears in individual steps or pieces.
Integration, on the other hand, is used when we want to add infinitely many extremely small pieces of a continuous quantity. Instead of adding separate values, integration accumulates values across an entire interval of a function. It is often used to find things like the area under a curve, total accumulated change, or the total effect of a continuously varying quantity. Conceptually, integration can be thought of as taking many very small sums and letting the pieces become smaller and smaller until they form a smooth, continuous total.
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#math #integration #3d #foryou #calculus
@mathswithmuza
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MAClass 12 Maths , Angle between Two vectors , Maths Viva , Maths Practical Exam 2026
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#reelsinstagram #class12maths #vectors #integration #reels
@maths_is_easy_insta
20.7M
SWIn calculus, “finding the volume of a solid” usually means using integration to calculate the volume of a 3D shape formed by rotating a 2D curve around an axis (called a solid of revolution). Since the shape is curved and doesn’t have a simple formula like a cube or sphere, you imagine slicing it into infinitely thin pieces (like tiny disks or cylinders), find the volume of each tiny slice, and then add them all together using an integral. Essentially, integration lets you sum up infinitely many small volumes to get the total volume of a complex 3D shape.
#math #calculus #mathjokes #stem
@swemattcodes
5.8M
_Cyou’ll never forget how to do integration by parts after this
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#math #physics #engineering #nerdgirl #uni
@_cyberanna_
909.3K
MAA sum is about adding up individual pieces that stay separate. You take a finite or countable set of values and combine them one by one, like adding the heights of a bunch of thin rectangles. Each term is distinct, and nothing happens in between those points. Sums naturally show up when you’re working with discrete data, step-by-step processes, or situations where the pieces are clearly separated, such as counting objects, adding probabilities in a table, or approximating areas using rectangles. The result depends on how many pieces you include and how wide or narrow each piece is.
An integral, on the other hand, treats the quantity as continuously changing. Instead of adding individual chunks, integration blends infinitely many tiny contributions into a single total. You can think of it as what happens when a sum is pushed to the extreme: the pieces become infinitely thin and the approximation turns exact. This makes integration the natural tool for finding areas under curves, total distance from a changing velocity, or accumulated quantities in physics and economics. While a sum feels like stacking blocks, an integral feels like filling a shape with no gaps at all.
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#math #maths #integration #foryou #3d
@mathswithmuza
2.8M
GIWe always say child learn from parents
But this time lets learn from children
#inclusion #autismawarenessmonth #autismacceptance #integration #occupationaltherapy
@giftedmindsmenage
1.1M
PHIntegration vs Summation.
Continuous vs Discrete.
Same sine curve — different mathematics.
What’s the difference between:
∫ sin(x) dx
and
Σ sin(x)
They may look similar, but they are fundamentally different.
1️⃣ Integration of sin(x)
∫ sin(x) dx = −cos(x) + C
Integration gives the continuous accumulated area under the sine curve.
Graphically:
You are measuring smooth area under a smooth wave.
2️⃣ Summation of sin(x)
Σ sin(xₖ)
Summation adds discrete sampled values of the sine function.
Graphically:
You are stacking vertical bars at chosen points.
Key Insight 💡
If you take more and more sample points,
the summation starts to approximate the integral.
This is the foundation of:
• Numerical methods
• Riemann sums
• Engineering simulations
• Signal processing
• Physics modelling
Continuous mathematics meets discrete computation.
That’s how calculus powers modern technology.
ENGAGEMENT 👇
If you increase the number of sample points,
does the summation get closer to the integral?
Yes or No?
Comment below.
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#RiemannSum
#EngineeringMath
#STEMEurope 🇪🇺
#AppliedMathematics
SignalProcessing
UniversityMath
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FutureEngineers
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DOPictographic signatures represent a sophisticated fusion of calligraphy and graphic design, transforming ordinary names into visual masterpieces. These artistic signatures go beyond traditional penmanship by converting letters into stylized symbols that capture a person’s identity, profession, or personality through deliberate visual integration.
The magic happens when natural loops and strokes of the alphabet are cleverly manipulated to form recognizable silhouettes like faces, birds, or objects while preserving the essence of the name itself. This delicate balance requires mastery of several fundamental elements that separate amateur attempts from professional signature design.
Fluidity and flow form the foundation of any effective pictographic signature. The strokes should appear natural and continuous, as if drawn in one graceful motion without interruption. When lines become too jagged or broken, the artistic effect feels forced rather than organic, breaking the visual harmony that makes these signatures so captivating.
Symbolic alignment ensures the imagery directly reflects the signer’s life and work. A photographer might incorporate a camera lens into their letter O, while a writer’s final stroke could elegantly taper into a quill shape. This personalization transforms a simple signature into a meaningful representation of one’s craft and passion.
The challenge lies in balancing legibility with abstraction. Despite the artistic flourishes, the signature must remain recognizable as a name. Typically, the first letter serves as the prominent anchor that holds the entire artistic shape together, while remaining letters flow seamlessly into the broader design, creating a cohesive visual identity that’s both functional and beautiful.
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Don’t forget to Share and Follow @dontlookback.ai
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#design #technology #graphicdesign #signatureart
calligraphy, visual design, typography, personal branding, logo design, artistic signatures, creative signatures, signature styles, handwriting art, custom signatures, brand identity, digital art
@dontlookback.ai
2.0M
QUThe Integral That Fools Everyone! 🧠✨
Have you ever looked at a math problem and thought, "Oh, this is just a basic formula," only to realize three pages later that you’re stuck in a loop? Welcome to the world of Sophomore’s Dream style integrals!
In this video, we’re breaking down the infamous \int \frac{1}{1+x^4} dx. On the surface, it looks like a standard power rule or tan-inverse situation, but the reality is much more beautiful (and complex).
The Secret Sauce:
To solve this, we don't just integrate. We manipulate!
We split it into two parts (I_1 and I_2).
We use the "Divide by x^2" trick to reveal a hidden structure.
We use the identity (x - 1/x)^2 to transform the denominator.
Why does this matter?
This specific problem is a favorite for competitive exams like JEE, Calculus BC, and University Math competitions because it tests your ability to see patterns, not just memorize formulas. It’s about Mathematical Intuition.#MathsEducation #CalculusTricks #Integration #STEM #MathIsBeautiful StudyInspiration AdvancedMath MathHacks CompetitiveExams LearningMathematics TheMathsMatriix
@quantumquesterr
6.3M
SM👀Dubai’s abandoned islands 🌎… What if they became this?
A visionary concept transforming the iconic
The World Islands into Royal Equestrian Island 🏇.
A horse-shaped island masterplan featuring a futuristic hippodrome, luxury villas and a 7-star hospitality concept.
🏨 High-end hospitality design
🏡 Geometric villa wings
🛥️ Private marina integration
✨ Ultra-modern parametric architecture
🎬 Hyper-realistic construction storytelling created with AI
Created by @smartcolorstudio .
Designed for:
🏗️ Real estate developers
🌍 Hospitality brands
💼 Visionary investors
We help transform early-stage architectural ideas into:
📊 Investor-ready presentations
🏆 Competition visuals
💎 Luxury marketing campaigns
🚀 High-impact launch content
Because iconic architecture deserves iconic storytelling.
Would investors stop scrolling for your next project? 👀
Dubai architecture | AI architecture | architectural visualization | Dubai real estate development | futuristic island resort | Dubai luxury resort design | hotel concept design | mega project | hospitality design UAE | AI real estate marketing | pre-construction visualization | investor presentation Dubai | luxury hotel development | concept masterplan Dubai | waterfront resort design | AI creative studio Dubai | architectural rendering AI | Dubai property developers | luxury island concept | AI cinematic visualization | visionary architecture
@smartcolorstudio
1.4M
ERCME zur Unterstützung von Kindern beim Gleichgewicht legt den Fokus darauf, zu verstehen, wie sich das Gleichgewicht im Kindesalter entwickelt 🧠👶. Dabei wird die natürliche Entwicklung der posturalen Kontrolle, der sensorischen Integration (vestibuläres, visuelles und propriozeptives System) sowie der motorischen Koordination im Laufe des Wachstums betrachtet 👀🦶✨.
Es wird betont, altersgerechte Meilensteine des Gleichgewichts zu erkennen, wie Spiel- und Bewegungserfahrungen die Gleichgewichtsfähigkeiten formen 🎈🤸♂️ und wie Faktoren wie Muskelkraft 💪, Reflexintegration sowie die Interaktion mit der Umwelt 🌍 die Stabilität beeinflussen.
Durch das Verständnis dieser entwicklungsbezogenen Grundlagen können Fachkräfte Verzögerungen oder Unterschiede besser erkennen 🔎📊 und Interventionen auswählen, die das Gleichgewicht im Einklang mit der jeweiligen Entwicklungsphase des Kindes fördern – anstatt Gleichgewicht als isolierte Fähigkeit zu betrachten 🧩🌱.
@erklarende.biologie
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