Q1. i) The above equations can be written as That is Solve by substitution Therefore, That is Integrate both sides ii) Solve the integral on the LHS by trigonometric...

Q1.

i)

The above equations can be written as

That is

Solve by substitution

Therefore,

That is

Integrate both sides

ii)

Solve the integral on the LHS by trigonometric substitution

Therefore,

Substitute sec(theta) and tan(theta) in terms of u

Substitute u in terms of y and x implies

iii)

Therefore, the solution becomes

Simplify

That is

iv)

Simplify

Squaring both sides

Hence, the solution is