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In order to calculate this integral we must use the sustitution provided. x=2siny. Firtsly I will differentiate to find the dx component of the integral, so dx/dy=2cosy hence, dx=2cosydy. Now for the limi...

To find potential points of intersection between the line and the circle, we need to solve the equations simultaneously. So, we substitute y = x - 7 into the equation of the circle: (x + 2)² + ...

x² + 5x = 5 Make equal to 0. x² +5x - 5 = 0 Recognise that you need to use the quadratic equation. (-b ± sqrt(b²-4ac))/2 sub in. (-5 ± sqrt(5²-41-5))/2...

Because the value, x and its inverse, -1/x should multiply together to give -1. This is proof that two lines are perpendicular (or having the same magnitude of gradient but opposite signs +/- ).

Area of square : Base x Height.

Area of Circle: π x (Radius)².

Looking at the diagram we are given the dimensions of the base or he...