Caculus

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:

..................................................................

(Total 6 marks)

2. (a) Find dx.

(4)

(b) Find .

(3)

(Total 7 marks)

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3. The acceleration, a m s-2, of a particle at time t seconds is given by

a = + 3sin 2t, for t ≥ 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...