MATH-11 · Undergraduate · ENGLISH · PLANNED
Build the picture, explain the rule, work an example, then justify it.
Study time is an initial activity estimate, excluding extra reading, revision and extended laboratory or project work. Videos and question bodies have not been produced by adding this outline.
Complete these courses or demonstrate equivalent knowledge. These are recommended prerequisites, not enforced enrolment locks.
YouTube playlist: ARK Mathematics | Calculus II: Integration and Series
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Sign in to save this learning pathPractical outcome: Recover distance from a changing-speed graph.
Explain riemann sums using a visual and one worked real-world example. Context: Recover distance from a changing-speed graph. End with a prediction or check-for-understanding.
Explain definite integrals using a visual and one worked real-world example. Context: Recover distance from a changing-speed graph. End with a prediction or check-for-understanding.
Explain fundamental theorem of calculus using a visual and one worked real-world example. Context: Recover distance from a changing-speed graph. End with a prediction or check-for-understanding.
Explain antiderivatives using a visual and one worked real-world example. Context: Recover distance from a changing-speed graph. End with a prediction or check-for-understanding.
Use the first concepts from this section. Recover distance from a changing-speed graph. Produce a labelled diagram, trace or calculation; explain each step and check one changed input.
3–6 questions on the preceding first-half concepts only: recall, visual interpretation, application and one plausible misconception. Explain each answer after submission.
Explain substitution using a visual and one worked real-world example. Context: Recover distance from a changing-speed graph. End with a prediction or check-for-understanding.
Explain integration by parts using a visual and one worked real-world example. Context: Recover distance from a changing-speed graph. End with a prediction or check-for-understanding.
Explain partial fractions using a visual and one worked real-world example. Context: Recover distance from a changing-speed graph. End with a prediction or check-for-understanding.
Explain improper integrals using a visual and one worked real-world example. Context: Recover distance from a changing-speed graph. End with a prediction or check-for-understanding.
Recover distance from a changing-speed graph. Work without the example, compare two cases, record assumptions and limitations, then self-review correctness, reasoning and clarity.
6–12 questions covering Riemann sums, Definite integrals, Fundamental theorem of calculus and the remaining section concepts, with cumulative retrieval from earlier sections. Include a new transfer problem; 70% unlocks progression.
Practical outcome: Estimate storage volume from cross sections.
Explain area between curves using a visual and one worked real-world example. Context: Estimate storage volume from cross sections. End with a prediction or check-for-understanding.
Explain disk method using a visual and one worked real-world example. Context: Estimate storage volume from cross sections. End with a prediction or check-for-understanding.
Explain washer method using a visual and one worked real-world example. Context: Estimate storage volume from cross sections. End with a prediction or check-for-understanding.
Explain shell method using a visual and one worked real-world example. Context: Estimate storage volume from cross sections. End with a prediction or check-for-understanding.
Use the first concepts from this section. Estimate storage volume from cross sections. Produce a labelled diagram, trace or calculation; explain each step and check one changed input.
3–6 questions on the preceding first-half concepts only: recall, visual interpretation, application and one plausible misconception. Explain each answer after submission.
Explain arc length using a visual and one worked real-world example. Context: Estimate storage volume from cross sections. End with a prediction or check-for-understanding.
Explain work as an integral using a visual and one worked real-world example. Context: Estimate storage volume from cross sections. End with a prediction or check-for-understanding.
Explain probability density integrals using a visual and one worked real-world example. Context: Estimate storage volume from cross sections. End with a prediction or check-for-understanding.
Explain numerical trapezoids using a visual and one worked real-world example. Context: Estimate storage volume from cross sections. End with a prediction or check-for-understanding.
Estimate storage volume from cross sections. Work without the example, compare two cases, record assumptions and limitations, then self-review correctness, reasoning and clarity.
6–12 questions covering Area between curves, Disk method, Washer method and the remaining section concepts, with cumulative retrieval from earlier sections. Include a new transfer problem; 70% unlocks progression.
Practical outcome: Approximate a sensor function with a controlled error.
Explain sequence convergence using a visual and one worked real-world example. Context: Approximate a sensor function with a controlled error. End with a prediction or check-for-understanding.
Explain geometric series using a visual and one worked real-world example. Context: Approximate a sensor function with a controlled error. End with a prediction or check-for-understanding.
Explain integral test using a visual and one worked real-world example. Context: Approximate a sensor function with a controlled error. End with a prediction or check-for-understanding.
Explain comparison tests using a visual and one worked real-world example. Context: Approximate a sensor function with a controlled error. End with a prediction or check-for-understanding.
Explain ratio test using a visual and one worked real-world example. Context: Approximate a sensor function with a controlled error. End with a prediction or check-for-understanding.
Use the first concepts from this section. Approximate a sensor function with a controlled error. Produce a labelled diagram, trace or calculation; explain each step and check one changed input.
3–6 questions on the preceding first-half concepts only: recall, visual interpretation, application and one plausible misconception. Explain each answer after submission.
Explain alternating series using a visual and one worked real-world example. Context: Approximate a sensor function with a controlled error. End with a prediction or check-for-understanding.
Explain absolute convergence using a visual and one worked real-world example. Context: Approximate a sensor function with a controlled error. End with a prediction or check-for-understanding.
Explain power series using a visual and one worked real-world example. Context: Approximate a sensor function with a controlled error. End with a prediction or check-for-understanding.
Explain taylor polynomials using a visual and one worked real-world example. Context: Approximate a sensor function with a controlled error. End with a prediction or check-for-understanding.
Explain taylor remainder bounds using a visual and one worked real-world example. Context: Approximate a sensor function with a controlled error. End with a prediction or check-for-understanding.
Approximate a sensor function with a controlled error. Work without the example, compare two cases, record assumptions and limitations, then self-review correctness, reasoning and clarity.
6–12 questions covering Sequence convergence, Geometric series, Integral test and the remaining section concepts, with cumulative retrieval from earlier sections. Include a new transfer problem; 70% unlocks progression.
Combine all three sections: Approximate a sensor function with a controlled error. Submit an original worked artifact, evidence or tests, assumptions and a reflection. Rubric: correctness, method, practical usefulness, reproducibility and communication. Self-reviewed, not certified.
6–12 balanced questions sampling every section of Calculus II: Integration and Series, including interpretation, calculation or reasoning, a misconception and a new application. Passing is 70%; review errors before retrying.
Visual constructions, worked problems and proofs. Guided work leads to an independent attempt, with a diagram, explanation, trace, calculation or tested artifact. Question bodies are generated when opened in your private learning path. Programming submissions are stored as text; the platform does not execute submitted code.
Use original or appropriately licensed datasets. Practical science activities use models or supplied data unless a qualified supervisor has reviewed a physical experiment.
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