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The function f(x) has the definite integral ∫14f(x)dx=6.
Write down the value of ∫143f(x)dx
Find the value of ∫01.52f(2x+1)−3dx
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Evaluate the integral ∫√3x+1dx
Hence find the value of ∫18√3x+1dx
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The velocity, vms−1, of a particle moving in a straight line is given by v(t)=(3−t)cost, for 0≤t≤6 seconds. The following diagram shows the graph of v as a function of t.
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Let t=q be the third time at which the particle changes direction.
Show that q=23π.
Find the distance travelled by the particle when t=q.
Find the acceleration of the particle when t=4.
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