Physical, Mathematical, Computer and Life Sciences Mathematical Sciences

Techniques for Indefinite and Definite Integrals Training

SAQA US 243832 | NQF 4 | Credits 5 | Duration 2 Days
From $832 per delegate

Description

This course equips learners with a comprehensive toolkit for solving both indefinite and definite integrals using a variety of techniques. Participants will develop proficiency in integration methods such as substitution, integration by parts, partial fractions, and trigonometric integrals, enabling them to apply these skills in mathematical modelling and problem-solving contexts.

Learning Outcomes

  • Apply substitution techniques to evaluate indefinite and definite integrals.
  • Analyze and select appropriate integration methods including integration by parts and partial fractions.
  • Evaluate definite integrals using the Fundamental Theorem of Calculus and numerical methods where applicable.
  • Demonstrate proficiency in integrating trigonometric, exponential, and logarithmic functions.
  • Design solutions to real-world problems by applying integration techniques in modeling contexts.
  • Implement error-checking strategies to verify the correctness of integrated results.

Target Audience

This course is designed for professionals, students, and individuals who require advanced calculus skills in fields such as engineering, physics, economics, or data science. It is suitable for those who have a foundational understanding of differential calculus and wish to deepen their integration techniques.

Prerequisites

None — open enrollment.

Course Outline

Day 1: Fundamental Techniques of Indefinite Integration

Objectives:
• Understand the concept of antiderivatives and the indefinite integral.
• Apply basic integration rules for polynomial, exponential, and trigonometric functions.
• Use substitution method for composite functions.
• Recognise and integrate simple rational functions.

Topics:
• Review of derivatives and antiderivatives.
• The indefinite integral and constant of integration.
• Power rule, constant multiple, sum/difference rules.
• Integration of exponential functions (e^x, a^x).
• Integration of basic trigonometric functions.
• Integration by substitution (u-substitution).
• Integration of simple rational functions (1/x, 1/(ax+b)).
• Practice problems with step-by-step solutions.

Day 2: Advanced Techniques and Definite Integrals

Objectives:
• Apply integration by parts for products of functions.
• Evaluate definite integrals using the Fundamental Theorem of Calculus.
• Compute areas between curves and volumes of revolution.
• Use partial fractions to integrate rational functions.
• Apply trigonometric identities for integrals.

Topics:
• Integration by parts: formula and selection of u and dv.
• Definite integrals: evaluation and properties.
• Fundamental Theorem of Calculus (Parts 1 and 2).
• Area between curves.
• Volumes of revolution: disk and washer methods.
• Integration using partial fractions.
• Trigonometric integrals using identities.
• Mixed practice and problem-solving session.

Practicals

No practicals for this training.

This course is made up of exercises and case studies delivered alongside the theory — no separate practical sessions are required to complete it.

Summatives

Each delegate is assessed continuously throughout the course and a final summative test at the end.

Daily Exercises — 30%

Every training day ends with a multiple-choice exercise scored out of 100%. The scores from each daily exercise are averaged across the duration of the course to produce a Daily Average mark, which contributes 30% to the final total.

Final Test — 70%

On the last day a final summative test is written. It is a multiple-choice paper with multiple-answer questions: each question may have more than one correct option, and a single wrong selection on a question marks the entire question wrong — no partial credit. The final test is scored out of 100% and contributes 70% to the overall mark.

Final Total
Component Out of Weight
Daily Average (multiple choice) 100% 30%
Final Test (multi-answer multiple choice) 100% 70%
Final Total 100%

All marks are recorded on the AATICD LMS and visible to each learner under their account.

Certificate

Certificate of Completion

Awarded to delegates who achieve an overall mark of 50% or higher on the Final Total (Daily Average 30% + Final Test 70%).

How it works
  • Certificates are auto-generated on the AATICD LMS as soon as the marks pass the 50% threshold.
  • Each certificate is a branded PDF with the delegate's name, the course title, the unit standard ID, NQF level, credits, and the date of issue.
  • You can download or print your certificate from your LMS dashboard at any time after issue — there's no reissue fee and no expiry date.
  • If you scored under 50% you can sit the final test again at the next scheduled session at no extra cost.
Where to find it

Sign in to the LMS, open your dashboard, and your certificates appear under My Certificates. Each entry has a View / Download button and a print option.

Training Discounts

Group discounts apply automatically — the more delegates you enrol, the greater the saving. Discounts are calculated at 3% per 5 delegates, scaling up to 40% off for 100+ delegates.

Delegates Discount
5 3% off
10 6% off
15 9% off
20 12% off
25 15% off
30 18% off
50 30% off
75 35% off
100 40% off

3% discount per 5 delegates, up to 40% off for 100+ delegates. Contact us for a custom group quote.

Upcoming Training Sessions
Online training — attend live sessions from anywhere via our virtual classroom.
Start End Delivery Season Price Action
Thu 10 Sep 2026 Fri 11 Sep 2026 Virtual Spring 2026 $832 Register
Mon 28 Sep 2026 Tue 29 Sep 2026 Virtual Spring 2026 $832 Register
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Mon 17 Jan 2028 Tue 18 Jan 2028 Virtual Summer 2027 $832 Register
On-Campus training — face-to-face sessions at our training venues across Africa and beyond.
Showing all 494 sessions across 26 venues
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Thu 06 Aug 2026 Fri 07 Aug 2026 Dubai, UAE Winter 2026 $4,217 Register
Thu 06 Aug 2026 Fri 07 Aug 2026 Johannesburg, South Africa Winter 2026 $1,571 Register
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Tue 11 Aug 2026 Wed 12 Aug 2026 Pretoria, South Africa Winter 2026 $1,247 Register
In-House training — we bring the trainer to your organisation, tailored to your team.
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Mon 14 Sep 2026 Tue 15 Sep 2026 Your Premises Spring 2026 $1,080 Register
Tue 06 Oct 2026 Wed 07 Oct 2026 Your Premises Spring 2026 $1,080 Register
Wed 28 Oct 2026 Thu 29 Oct 2026 Your Premises Spring 2026 $1,080 Register
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Wed 10 Mar 2027 Thu 11 Mar 2027 Your Premises Autumn 2027 $1,080 Register
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Mon 22 Mar 2027 Tue 23 Mar 2027 Your Premises Autumn 2027 $1,080 Register
Tue 15 Jun 2027 Wed 16 Jun 2027 Your Premises Winter 2027 $1,080 Register
Wed 07 Jul 2027 Thu 08 Jul 2027 Your Premises Winter 2027 $1,080 Register
Thu 29 Jul 2027 Fri 30 Jul 2027 Your Premises Winter 2027 $1,080 Register
Mon 13 Sep 2027 Tue 14 Sep 2027 Your Premises Spring 2027 $1,080 Register
Tue 05 Oct 2027 Wed 06 Oct 2027 Your Premises Spring 2027 $1,080 Register
Wed 27 Oct 2027 Thu 28 Oct 2027 Your Premises Spring 2027 $1,080 Register
Thu 16 Dec 2027 Fri 17 Dec 2027 Your Premises Summer 2027 $1,080 Register
Mon 03 Jan 2028 Tue 04 Jan 2028 Your Premises Summer 2027 $1,080 Register
Tue 25 Jan 2028 Wed 26 Jan 2028 Your Premises Summer 2027 $1,080 Register
Training Discounts
Delegates Discount
5 3% off
10 6% off
15 9% off
20 12% off
25 15% off
30 18% off
50 30% off
75 35% off
100 40% off

3% off per 5 delegates, up to 40% for 100+

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