Tough Integration Question 3

Let S = .

Using the substitution x = cos² ϴ , show that .

Hence, find the exact value of S in terms of π .

(Note: Check the notes on the next page about definite integrals for integration using substitution)

Solution:

Tough Integration Question 2

Let R =  (4x^2 + 9x - 8) / (2x^2 + 3x - 2 ) . By expressing R in partial fraction, show that 

Solution:

Tough Integration Question 1

Let R = (4x^2 + 9x - 8) / (x^2 + 5x + 2 ). By expressing R in partial fraction,

and solve

Solution: