3.46: Definite cosine integral and rational integral

0606/22/M/J/24 — Question 2 · 7 marks

(a)
Evaluate π/3π/24cosxdx\displaystyle\int_{\pi/3}^{\pi/2} 4\,\mathrm{cos}\,x\,\mathrm{d}x. You must show all your working.
[4]
(b)
Find (4x33x+1)dx\displaystyle\int(4x^{3}-3x+1)\,\mathrm{d}x.
[3]