SL M6 Calculus 2 - Integration Assignment 59 Marks
B.Coulton 1
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1. It is given that = x3+2x - 1 and that y = 13 when x = 2.
Find y in terms of x.
Working:
Answer:
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(Total 6 marks)
2. (a) Find dx.
(4)
(b) Find .
(3)
(Total 7 marks)
Calculator Optional
3. The acceleration, a m s-2, of a particle at time t seconds is given by
a = + 3sin 2t, for t âÂÂ¥ 1.
The particle is at rest when t = 1.
Find the velocity of the particle when t = 5.
(Total 7 marks)
4. (a) Find the equation of the tangent line to the curve y = ln x at the point (e, 1), and verify that the origin is on this line.
(4)
(b) Show that (x ln x - x) = ln x.
(2)
(c) The diagram shows the region enclosed by the curve y = ln x, the tangent line in part (a), and the line y = 0.
Use the result of part (b) to show that the area of this region is e - 1.
(4)
(Total 10 marks)
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5. In this question s represents displacement in metres and t represents time in seconds.
The velocity v m s-1 of a moving body is given by v = 40 - at where a is a non-zero constant.
(a) (i) If s = 100 when t = 0, find an expression for s in terms of a and t.
(ii) If s = 0 when t = 0, write down an expression for s in terms of a and t.
(6)
Trains approaching a station start to slow down when they pass...