Min, Max and Trapezoidal Help! (1 Viewer)

[Lemiixem]

Q11.
A) Find the turning points on the curve y = sin2x + 3 over the domain 0<x<Pie
b) What is the maximum value of the curve.

Q16. Use the trapezoidal rule with 4 subintervals to find, correct to 3 decimal places, an approximation to the volume of the solid formed by rotating the curve y = sin x about the x-axis from x = 0.2 to x = 0.6

 

[Carrotsticks]

For the first one you actually need not use Calculus.

We note that the turning points for the normal sine curve (over one period) occur at (pi/2,1) and (3pi/2,-1). Since we are dealing with sin2x (which has everything 'squished' into half), the new turning points become (pi/4,1) and (3pi/4,-1).

However we are then shifting the curve up by 3 units, so the turning points are (pi/4,4) and (3pi/4,2). We want the maximum, which is clearly the y value of the first one ie: 4.


For the second one, this is an interesting problem. I won't go into too much detail as to why this is the case but to get the volume, square all the y values in the table and then multiply by pi.

Then plug into the formula.

Quick reasoning is because volume is