Couple of TRIG FUNCTION questions that I need help with

[preliminary17hsc18]

Hi all,

Just had a few trigonometric function questions that I need some help with:
1. Find the exact volume of a solid formed when the curve y = sec2x is rotated about the x axis between x = 0 and x = pi/8
2. Show that the curve y = sin2x and the line y = 4x/pi intersect at x = pi/4 (I can do this part). Find the area bounded by the curve y= sin2x and the line y = 4x/pi in the 1st quadrant (answer in terms of pi)


Thanks in advance!

[RuiAce]

The first two are literally just straight applications of the formulae \(\int \cos ax \,dx = \frac{1}{a}\sin ax\) and \(\int \sec^2 ax\, dx = \frac{1}{a}\tan ax\).



Remark: One thing awkward about this one is trying to figure out which graph goes on top. The easiest way I can think of is really by just testing points between 0 and pi/8 explicitly. Most likely in the HSC they'd give the graph.