Calculus 2 (Integral Calculus):

Let’s step into the world of areas, totals, and accumulation. You’ll learn how integrals measure things that build up — distance, volume, energy, probability — and see how this idea extends the work you did with derivatives.

We’ll explore the reverse of differentiation. You’ll learn integration rules, substitution techniques, and how antiderivatives help us understand entire families of functions.

Here, calculus becomes a complete system. You’ll learn how definite integrals measure accumulated change and how the Fundamental Theorem connects derivatives and integrals in one elegant bridge.

You’ll build fluency with powerful tools: integration by parts, substitution, partial fractions, trigonometric substitutions, and special integrals. These techniques turn complex expressions into solvable structures.

Some integrals stretch toward infinity or involve singularities — yet they still have meaning. You’ll learn how to evaluate improper integrals and understand when they converge or diverge.

This is where integral calculus becomes visual and powerful. You’ll use integrals to find areas, volumes (washer, shell, and slicing methods), arc lengths, surface areas, and quantities from physics such as work and mass.

You’ll encounter your first differential equations — separable and linear first-order types — and learn how integrals solve them. This opens the door to modeling populations, motion, and physical systems.

You’ll explore infinite processes — geometric series, Taylor polynomials, power series, and convergence tests. This is where calculus begins to resemble the language of analysis.

If you’re ready to go further, we can dive into multivariable integration, vector fields, Fourier ideas, or advanced problem-solving. Private sessions transform calculus into a landscape open for exploration.