📊 Integration & Area Under Curve Visualizer
CalculusWhat's happening? More rectangles = better approximation. The Riemann sum converges to the exact integral as n→∞. This is the fundamental idea of integration.
Integration: 8-10 questions every year.
JEE tests fundamental theorem, substitution, by parts, area.
Key formulas
Integration / Area Under Curve Formulas
Definite
integral a to b f(x)dx = F(b) - F(a)
Fundamental theorem
Area
A = integral f(x)dx
Between curve and x-axis
By parts
integral u dv = uv - integral v du
ILATE rule
Substitution
u = g(x), du = g'(x)dx
Change of variable
Step-by-step problem solving
How to solve maths problems in JEE
- Identify integral type
- Choose method: substitution, parts, partial fractions
- Find antiderivative F(x)
- Definite: F(b)-F(a). Area: check sign
Common JEE mistakes
What students get wrong
Missing + C
Indefinite needs + C, definite doesn't
Wrong area bounds
Split if curve goes below x-axis
Substitution dx
Replace dx with du/g'(x)
By parts order
ILATE: Inverse, Log, Algebraic, Trig, Exp
FAQs
Integration / Area Under Curve Questions
Fundamental theorem?
integral a to b f(x)dx = F(b) - F(a) where F' = f
Area between curves?
integral (top - bottom) from left to right intersection
When substitution?
Composite function with derivative present
LIATE rule?
Choose u: Log, Inverse, Algebraic, Trig, Exp