🔍 What Are Integrals?
Integrals are a core concept in calculus used to calculate areas, volumes, and quantities like total accumulation. They are the reverse process of differentiation, often called antiderivatives. For example, ∫2x dx = x² + C, where C is the constant of integration.
📈 Key Applications
- Area under curves: Use definite integrals to find the area between a function and the x-axis
- Accumulation: Calculate total distance traveled from velocity functions
- Volume of revolution: Compute volumes of 3D shapes generated by rotating curves
- Physics: Determine work done or center of mass
📝 Practice Problems
- Evaluate ∫(x² + 3x) dx from 0 to 2
- Find the indefinite integral of e^(2x) + 5cos(x)
- Calculate the area between f(x) = x³ and g(x) = x² from x=0 to x=1
- Solve ∫(3x² - 4x + 1) dx using substitution
🧩 Tips for Mastery
- 📌 Start with basic antiderivatives (polynomials, exponentials)
- 📌 Practice sketching graphs to visualize the area being calculated
- 📌 Use this resource to review derivative rules (since integrals rely on inverse operations)
- 📌 Check your answers by differentiating the result
📚 Expand Your Knowledge
For advanced techniques like integration by parts or partial fractions, visit Integral Techniques Deep Dive.