INTEGRATION RULE COPIED! ♾️

Integration Rule ♾️

∫ xⁿ dx =
xⁿ⁺¹ n + 1
+ C
Condition: n ≠ -1

Integration Symbol Guide ♾️

∫
Integral Sign

The "S" shape represents 'Summation'. It tells you to find the antiderivative.

f(x)
The Integrand

The function inside the integral that you are actually integrating.

dx
Differential

Indicates the variable of integration (with respect to x). It's like a tiny width.

n
The Power

The exponent of the variable. In power rule, we add 1 to this value.

+ C
Integration Constant

Added to indefinite integrals to represent any possible constant value.

a
Lower Limit

The starting point of integration for definite integrals (area calculation).

b
Upper Limit

The end point of integration for definite integrals.

F(x)
Antiderivative

The result of the integration process (the capital F function).

[a, b]
Interval

The specific range on the x-axis where the area is being measured.

Legacy of the Integral 📜

∫

250 BC | EXHAUSTION

Archimedes used the 'Method of Exhaustion' to find the area of circles and parabolas. This was the primitive root of integration long before calculus was official!

1660s | CO-FOUNDERS

Isaac Newton and Gottfried Leibniz independently discovered the Fundamental Theorem of Calculus. Leibniz actually gave us the elegant ∫ symbol we use today.

1850 AD | RIGOR

Bernhard Riemann provided the formal definition of the integral (Riemann Sum), allowing mathematicians to calculate areas under even the most complex curves.

"Did you know? Integration is the secret behind calculating the volume of planets, the flow of electricity, and even the probability of winning a game!"