Free · No account · Step-by-step learning
York University · Keele · applied calculus II
York University SC/MATH1014 — Applied Calculus II
Continue from differential calculus with selected definite integrals, substitutions and integration by parts. York’s sequence and series material remains outside these short sets.
16 original question families · 48 parameter instances
Practise this course →Course alignment and coverage
Current official public course description checked 25 October 2026. No current section-level or weekly syllabus was publicly verified; topic alignment below does not claim a teaching sequence or assessment coverage.
Across this collection: 156 distinct original families and 468 parameter instances. Courses share topic banks; translations and shared mappings are not extra questions.
Supported learning objectives
Polynomial antiderivatives
Reverse the power rule and use a stated constant or initial value. Exact fractional coefficients are supported.
Definite integrals and average value
Evaluate elementary polynomial integrals, distinguish signed accumulation and compute an average value.
Selected integration substitutions
Change variables and both bounds in elementary polynomial, logarithmic and trigonometric definite integrals.
Selected integration by parts
Evaluate four elementary definite-integral patterns with one or two integrations by parts; numerical answers only.
What is not covered
No general integration strategy, partial fractions, trigonometric substitution, improper integrals, infinite sequences/series, convergence proofs or full applications. Previous calculus is required by York; check the listed alternatives.
An original worked example
Find F(x) with F′(x)=6x² and F(0)=0. Enter the polynomial.
Worked solution
Answer: 2x^3
- A general primitive is 2x³+C.
- F(0)=0 gives C=0, hence F=2x³.
Official course sources
Independent, original, free self-study practice. Not affiliated with or endorsed by this university; these are not official exam questions. Topic alignment does not establish transfer credit, a current section’s weekly syllabus, full course coverage or a grade prediction. Follow your instructor’s rules and use official course materials for assessed work. No live AI chat or paid access is required.