Calculus: ready solutions

This section contains solutions to typical calculus problems with step-by-step explanations. Each solution includes the condition, a full solution with comments, and the answer.

Sections

• Antiderivative and integral — Finding antiderivatives, indefinite integrals, substitution, integration by parts.
• Definite integral — Rational, trigonometric, and irrational integrands.
• Improper integrals — Convergence of improper integrals, comparison tests.
• Double integrals — Evaluation of double integrals and their applications (mass of a plate, area).
• Triple integrals — Evaluation of triple integrals, transformation to cylindrical and spherical coordinates.
• Line integrals — Line integrals of the first and second kind.
• Surface integrals — Surface integrals of the first and second kind, Ostrogradsky-Gauss theorem.
• Elements of field theory — Curl, divergence, gradient of vector and scalar fields.