Question

1. Evaluate the integral: ( 4 Marks)

a)

b)

Answer 1

\[a) \int\limits_{0}^{\pi/4} \cos ^{2} \left( 4t-\pi/4 \right)dt\]

Answer 2

\[b ) \int\limits_{0}^{\pi/2} 3\sin x \cos x \div \sqrt{1+3\sin ^{2}} x\]

Answer 3

for (a) use the 1/2 angle formula (then substitution)
for (b) use substitution \[u=1+3\sin^2(x)\]