Exercise 1 from note (Question 3)

Find the area of the shaded region for each of the following graphs.

Solution:

9709/Oct Nov/2009/32/Q6

6i) Use the substitution x = 2 tan q to show that

6ii) Hence find the exact value of

Solution:

Reference: PYQ - Oct/Nov 2009 Paper 32 Q6

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Integration Question 24

Integrate e^2x cos x

Solution:

Integration Question 15 and Question 20

a) Integrate x^m ln x
b) Integrate x^1/2 ln x

Solution:

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: