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Basic Integration

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Examples, solutions, videos, activities and worksheets that are suitable for A Level Maths to help students answer questions on integration.

The following diagrams show some examples of Integration Rules: Power Rule, Exponential Rule, Constant Multiple, Absolute Value, Sums and Difference. Scroll down the page for more examples and solutions on how to integrate using some rules of integrals.

Integral Rules

Basic Integration
How to find antiderivatives, or indefinite integrals, using basic integration rules.
How to integrate a polynomial with the power rule?
How to integrate negative powers of x, fractional powers of x, and radicals/roots
How to integrate x-1, or 1/x, with the log rule How to use algebra to rewrite before integrating, separate the numerator of a fraction, or expand a product in order to use the power rule.
Basic Trig and Exponential examples that use rules from the Table of Integrals, as well as trig identities.

Edexcel C1 Core Maths June 2007 Question 9
The curve C with equation y = f(x) passes through the point (5, 65). Given that f'(x) = 6x2 - 10x - 12,
(a) use integration to find f(x).
(b) Hence show that f(x) = x(2x + 3)(x - 4).
(c) In the space provided on page 17, sketch C, showing the coordinates of the points where C crosses the x-axis. A-Level Maths Edexcel C1 June 2009 Q3b
Worked solution to the above core 1 question on integration.
y = 2x3 + 3/x2, x ≠ 0 A-Level : Edexcel : C1 June 2008 Q1
Short question on basic integration.
Integrate 2 + 5x2 A-Level Edexcel C2 June 2007 Q1
Worked solution to this question on integration.

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