## Integration

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### IN1 Antidifferentiation

Antidifferentiation (also called integration) is the opposite operation to differentiation. If you have the differentiation of a function, you can then obtain the original function via integration (...

### IN2 Integration of polynomials

How do you integrate a polynomial where x is raised to a power? We saw this in the previous section on antidifferentiation. But how do you integrate a linear expression in brackets where the whole...

### IN3.1 Integration of functions of the form m over (ax+b)

How do you integrate a logarithm? How do you integrate an exponential function? How do you integrate a trigonometric function?

### IN3.3

### IN3.3 Integration of exponential functions

How do you integrate a logarithm? How do you integrate an exponential function? How do you integrate a trigonometric function?

### IN3.4

### IN3.4 Integration of trigonometric functions

How do you integrate a logarithm? How do you integrate an exponential function? How do you integrate a trigonometric function?

### IN5 Area under a curve

An area under a curve might be above the axis (and therefore positive). But sections might also be below the axis (and therefore negative).

### IN6 Integration by substitution

An expression that is composed of two functions (say an algebraic expression nested within a trigonometric expression) can be complicated to integrate. You can simplify this by substituting a single...

### IN7 Integration using partial fractions

How do you integrate an expression when there is an algebraic expression in the numerator and denominator of a fraction? Integrating using partial fractions helps you to solve this problem.

### IN8 Integration by parts

If you can consider your expression to be a product (i.e. Multiplication x) of two functions, you can integrate this using Integration by parts. This reflects the product rule in...

### IN9 Double integrals

Integrating will find the area between the curve and the x-axis (horizontal axis). We learned in IN4 Definite integrals how to limit this to a section of the x axis.

### Integration

Integration is vital in engineering. It is the key mathematical tool for finding the centre of mass or the surface area of a body. Integration is also called antidifferentiation.