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Using Binomial expansion or Pascal's triangle, expand (1+x)^4 to get 1+4x+6x^2+4x^3+x^4. Then, by substituting √y for x, get 1 + 4y^1/2 + 6y +4y^3/2 +y^2. Then, using the rules of integration, the expansi...

4 sin(x) – 8 cos(x)= Rsin(x-a) here use double angle formula

4 sin(x) – 8 cos(x)= Rsin(x)cos(a)-Rcos(x)sin(a) Rearrange so in same format as LHS

4 sin(x) – 8 cos(x)= Rcos(a)sin(x)-Rsin(a)cos...

(a) To confirm that point P lies on L, we must substitute x = 3 into the equation and see if we get y = -1. y = 5 - 2(3) = -1, therefore P lies on the line L (b) The gradient of the perpendicular line is ...

differentiate 6x^3 + 2x^2 + 1 = 18x^2 + 4x

To determine stationary point set second derivative to zero

2nd derivative =36x + 4

36x + 4 = 0 therefore x = -4/36 = -1/9

x is -ve t...

This is a question which tests your knowledge of how to use trigonometric identities as well as integration. As there is no way to immediately integrate tan^2(x) using well known trigonometric integrals a...