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Consider the function g defined by g(x)=2−4sin2x. The following graph shows the curve y=g(x) for 0<x<23π.
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The graph of y=g(x) intercepts the x-axis at a, b, c and d, as shown.
Find the values of a,b,c and d.
In the diagram above, the region enclosed by the curve of y=g(x) and the x-axis between x=b and x=c is shaded.
Show that the area of the shaded region is 34π+2√3.
The diagram below shows a circle of radius r circumscribing a shape whose area is 34π+2√3.
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Find the value of r.
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A particle X moves in a straight line. Its velocity, v feet per second, from the origin after t seconds is given by v(t)=3t2−12t+9.
State the initial velocity of particle X.
Find the time(s) at which particle X changes directions.
The velocity of X reaches a minimum when t=q.
Show that v(q)=−3.
Let a be the acceleration of particle X.
Find a when t=q+1.
Particle X starts at the origin when t=0.
Find the total distance travelled by the particle when t=q.
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