🕹️ Practice arcade

⚡ Derivative Readiness Sprint

Power, product, quotient, chain, $\sin$, $e^x$ — as many derivatives as you can find in 90 seconds.

⚡ Integration Readiness Sprint

$u$-substitution, FTC Part 2, a Riemann sum, L'Hopital's rule — the toolkit this course is about to lean on.

⚡ Definite Integral Sprint

Net signed area, FTC Parts 1 and 2, additivity — as many definite integrals as you can evaluate in 90 seconds.

⚡ Average Value and Inverse-Trig Integrals

Average value, the point that attains it, and integrals landing on $\arctan$ — 90 seconds.

⚡ Area and Volume Sprint

Area between curves, cross-sectional slicing, disks, shells — as many as you can set up and evaluate in 90 seconds.

⚡ Applications of Integration Sprint

Centroids, expected value, hydrostatic force, probability density normalization, and surface area of revolution — 120 seconds.

⚡ Work Sprint

Constant forces and Hooke's Law springs — set up the work integral and evaluate, 60 seconds.

⚡ Techniques of Integration Sprint

Parts, tabular integration, Simpson's Rule, the trapezoidal rule, improper integrals — the toolkit, 120 seconds.

⚡ Trig & Substitution Techniques Sprint

Trig integrals, trig substitution, half-angle substitution, and partial fractions integration — 2.5 minutes.

⚡ Differential Equations Sprint

Euler's method, exponential growth/decay, initial value problems, separable equations, integrating factors, Newton's Law of Cooling — 120 seconds.

⚡ Parametric Equations Sprint

Find dy/dx, locate a vertical tangent, write a tangent line, and compute speed — 120 seconds.

⚡ Polar Calculus Sprint

Tangent slopes, area enclosed by a polar curve, symmetry tests, and curve intersections — 120 seconds.

⚡ Sequences and Series Sprint

Sequence terms and limits, geometric and telescoping sums, the Divergence Test, and series algebra — 120 seconds.

⚡ Convergence Tests Sprint

Integral Test tail integrals, p-series exponents, comparison-test setups, alternating-series error bounds, and Ratio/Root Test limits — 120 seconds.

⚡ Power and Taylor Series Sprint

Radius of convergence, endpoint values, geometric power series, term-by-term coefficients, Taylor coefficients, Maclaurin recall, and the Lagrange remainder bound — 120 seconds.

⚡ Taylor Series Applications Sprint

Maclaurin library coefficients, series substitution and multiplication, numerical approximation with error bounds, series-based limits, term-by-term integration, and Euler's formula — 120 seconds.

⚡ Polar Conics Sprint

Evaluate a conic's polar equation at a given angle — 60 seconds.

⚡ Sequences and Power Series Readiness Sprint

Sequence limits, the ratio test, geometric series, and a power series' own coefficients and center — the calc-II toolkit chapter 8 leans on.

🎯 Before You Integrate

$+C$, what the $\int$ notation actually means, spotting a chain-rule shape, classifying an indeterminate form — six in a row.

🎯 What Makes an Antiderivative

Verify an antiderivative by differentiating, not integrating again — four in a row.

🎯 Symmetry and Sign

Odd/even symmetry, a negative integrand's sign, what the Mean Value Theorem actually claims — five in a row.

🎯 Definite Integral Properties

Reversing the bounds negates the whole answer — four in a row.

🎯 Which Method, Which Variable?

dx or dy, disk radius vs. diameter, and which volume method actually fits the region — five in a row.

🎯 Pick the Technique

Match the integrand's shape to its technique, and know which grid points a numerical rule weights — five in a row.

🎯 Order and Stability

A differential equation's order, and whether an autonomous equilibrium is stable or not — five in a row.

🎯 Trace, Tangent, and Speed Concepts

Vertical vs. horizontal tangents, the parametric second derivative, and what forces speed to zero — six in a row.

🎯 Parametric Curve Basics

Plot a point from a parametrization, and know what trace vs. parametrization means — four in a row.

🎯 Eliminate the Parameter

Convert a parametrization into a single equation in x and y — four in a row.

🎯 Polar Coordinate Basics

What r and theta mean, negative r, and converting between polar and rectangular — five in a row.

🎯 Recognize the Polar Curve

Circles, roses, and cardioids — match the equation's shape to its family, four in a row.

🎯 Sequence and Series Concepts

Recursive vs. explicit, oscillating divergence, ratio bounds, telescoping cancellation, the Divergence Test's one-way logic, convergent-plus-divergent — six in a row.

🎯 Convergence Test Concepts

Test hypotheses, the p=1 and L=1 thresholds, comparison direction, absolute vs. conditional convergence, and picking the right test by shape — six in a row.

🎯 Power and Taylor Series Concepts

What R actually guarantees, classifying endpoints, term-by-term calculus, what T_n matches, the Maclaurin center, the remainder bound's inputs, and when the binomial series terminates — six in a row.

🎯 Taylor Series Applications Concepts

Recognizing the library series, substitution vs. scaling, dividing series order by order, why series integration works, Euler's identity, and when linearization is valid — six in a row.

🔗 Inverse Trig Derivatives Mastery

Differentiate arcsin and arctan of a linear inner function.

∫ Integral Additivity Mastery

Split and rejoin integrals over adjacent intervals — four in a row.

🔑 Initial Value Mastery

Integrate, then use the initial condition to pin down $C$.

∫ Accumulation Function Mastery

Evaluate an accumulation function built from a constant rate.

📏 Arc Length Mastery

Find the arc length of a line segment over an interval.

🎯 Geometric Series Check

A geometric distribution's own validity leans on this convergence test — get it right four times in a row.