∫ Calculus

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Differentiate and integrate step by step, evaluate limits with L’Hôpital’s rule, find partial and implicit derivatives, and expand functions as Taylor series.

Every answer is checked (integrals are differentiated back) and shown with the rules used, so you can follow the working for school, JEE, IB, A-level and university calculus.

Derivative

Differentiate any function step by step — power, product, quotient and chain rules — with higher derivatives, the value at a point and the tangent line.

Integral

Find the indefinite integral (antiderivative) of a function step by step — substitution, integration by parts, partial fractions and trig identities — checked by differentiating.

Definite Integral

Evaluate a definite integral between two limits — exact answer by the Fundamental Theorem of Calculus where possible, plus the decimal value, total area and average value.

Double Integral

Evaluate double integrals ∬ f(x, y) over rectangles and regions with curved limits — exact iterated integration step by step, checked numerically.

Partial Derivative

Find partial derivatives ∂f/∂x, ∂f/∂y, second and mixed partials of multivariable functions, the gradient and values at a point.

Limit

Evaluate limits as x approaches a number or infinity — direct substitution, L’Hôpital’s rule for 0/0 and ∞/∞, one-sided limits and a table of values.

Series

Find the sum of an infinite series and test whether it converges or diverges — n-th term, ratio, alternating series and p-series tests — with partial sums.

Summation

Evaluate sigma notation sums Σ from a lower to an upper limit, with exact fractions, the expanded terms and the closed-form formula for polynomial terms.

Taylor Series

Expand a function as a Taylor or Maclaurin series up to any order, with the derivatives and coefficients in a table and a graph of the approximation.

Implicit Differentiation

Find dy/dx for equations like x² + y² = 25 or x³ + y³ = 6xy, step by step, with the slope and tangent line at a point and the second derivative.

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