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Integration

Integration involves knowing about:

Know and use The Fundemental Theorem of Calculus;

Integrate x^n (excluding n=-1) and related constant multiples, sums and differences;

Integrate e^kx, a^kx, sin kx, cos kx and related constant multiples, sums and differences;

Evaluate definite integerals;

Use definite integrals to find the area under a curve and the area between two curves;

Understand and use integration as the limit of a sum;

Carry out cases of integration by substitution and integration by parts;

Understand that integration by substitution is the inverse of the chain rule and integration by parts is the inverse of the product rule;

Integrate using partial fractions that are linear in the denominator;

Evaluate the analytical solution of simple first order differential equations with separable variables and find particular solutions;

Understand using factorisation to find a solution by separation of variables;

Interpret the solution of a differential equation in the context of solving a problem including identifying limitations of the solution (possibly with links to kinematics).

Short Introduction to Integration

This video gives some brief background information about Integration.

What is Integration?

This video gives a brief introduction to Integration.

Area under a cos function graph

This video shows you how to integrate a simple cosine function.

What is Integration?

This video shows you how to integrate a simple exponential function.