Calculus Tools, Guides, Practice and Formulas

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Solve Open the calculus solver Enter a derivative, integral, or limit and inspect the result, method, conditions, and check.
Calculate Use a focused calculator Choose derivative, integral, or limit controls for a narrower task.
Learn Study a calculus method Connect formulas to decisions through complete examples and checks.
Practise Choose calculus practice Follow a worked problem, identify the first uncertain step, and build a focused review sequence.
Reference Look up calculus formulas Find formulas, conditions, symbols, examples, and a printable PDF.

Calculus studies change and accumulation. This hub organizes the tools and explanations needed to work with limits, derivatives, and integrals.

Resource directory

Explore every calculus resource

Choose one focused page. New tools and guides are added here automatically when they are approved for this subject.

Solvers and calculators

Learning guides

Practice

Practise calculus with a clear purposeBegin with one complete problem, then use the review plan to practise the method choices that need attention.

Formula references

Calculus formulasScan the core rules, check when each one applies, and download the same structured reference as a PDF.

Concept map

Ideas that organize this subject

Limits

A limit describes the value a function approaches and provides the language for continuity and instantaneous change.

\lim_{x\to a}f(x)=L

Derivatives

A derivative measures instantaneous rate of change and the slope of a tangent line.

f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}

Integrals

A definite integral measures signed accumulation; an indefinite integral represents a family of antiderivatives.

\int_a^b f(x)\,dx

The central connection

The Fundamental Theorem links accumulation and differentiation, turning many definite integrals into endpoint evaluations.

\int_a^b f(x)\,dx=F(b)-F(a)

Suggested order

A practical learning sequence

1
Secure functions and limits
Review notation, domain, graphs, algebraic simplification, and how a function behaves near a point.
2
Learn derivatives as rates
Connect the limit definition to derivative rules, graphs, motion, and optimization.
3
Learn integrals as accumulation
Build from Riemann sums to antiderivatives, the Fundamental Theorem, and integration methods.
4
Mix ideas through applications
Use derivatives and integrals together in modeling, approximation, area, volume, and differential equations.

Common questions

Calculus FAQ

Where should I start learning calculus?

Start with functions, graphs, and algebra, then learn limits before derivative and integral techniques. If you already know the basics, choose the tool or guide that matches the problem in front of you.

Are derivatives and integrals opposites?

They are inverse processes under the conditions of the Fundamental Theorem of Calculus. The relationship is precise for continuous functions and appropriate antiderivatives, not a rule to apply without checking conditions.

Can I use these pages for homework?

Use the worked reasoning to understand or check your own work. Whether a calculator is allowed in an assignment or exam depends on your teacher and the rules for that assessment.

What mathematics should I review first?

Comfort with algebra, functions, exponents, logarithms, trigonometry, and graph interpretation prevents most avoidable calculus errors.

Continue learning

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