cameroon gce A level June 2009 further mathematics 2
cameroon gce A level June 2009 further mathematics 2
Find the general solution to the differential equation
π₯
ππ¦/ππ₯ – π¦ = π₯2
.
2.a. Express into partial fractions
π(π₯) =(π₯2 + 1)(π₯ – 1)2
b. Hence, evaluate β«23 π(π₯) ππ₯.
c. Given that
πΌπ= β« sinπ ππ20ππ,
show that for π β₯ 2, πΌπ = (ππ-1) πΌπ-2. Hence, evaluate πΌ5.
3.
a. Using the definition of sinh π₯ in terms ππ₯, show that sin-1 π₯ = ln(π₯ + β1 + π₯2).
Hence or otherwise, show that
β« β9π₯12 + 4
