Learning Lab

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...

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

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

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

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

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...

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.

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...

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 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.

Transforms are another means of solving some differential equations that may prove too difficult to solve using other methods.

A matrix is an array of numbers. This module discusses matrices, their order, row and column matrices, square matrices and the identity matrix.

Eigenvalues and eigenvectors are used to understand how buildings, structures and automobiles react in real life. They also provide insights into many mathematical areas.

Matrices of the same shape (same number of rows and columns) may be added/subtracted by adding/subtracting the corresponding elements.

To multiply two matrices A and B, the number of columns in A must equal the number of rows in B.

The determinant of a matrix can only be calculated for a square matrix and is used in many aspects of mathematics/engineering/physics.

It is helpful to understand the definition of a number of different types of “special” matrices.

Systems of linear equations may be solved using elementary row operations. This is sometimes called Gaussian elimination.