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First we must multiply out the brackets, using FOIL (first, outer, inner, last). This gives f(x) = -x^3 + 5x^2 - 3x + 15. Alternatively you could leave the brackets as they are, and use the product rule t...

Differentiation is a very important tool for mathematicians. Although finding the gradient of a line can seem to lack a point, it does have some very important applications. For example, in mechanics the ...

1. y = cos2θ . 2) cos2θ = 1 - 2sin²θ. 3) x = 2sinθ. 4) x² = 4sin²θ. 5) (1/2)x² = 2sin²θ. 6) y = 1 - (1/2)x².

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First, my approach is to ask student to count the squares on the area under a curve. This process is tedious, and only gives an estimation. Next, I show them the formula to do integration, and immediately...