Edexcel GCE Core Mathematics C4 Advanced June 2013
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C4 Edexcel Core Mathematics June 2013 Question 1
Integration by Parts
1. (a) Find ∫x2 ex dx
(b) Hence find the exact value of
Binomial Expansion for non-integer powers
2. (a) Use the binomial expansion to show that
(b) Substitute x = 1/26 into
to obtain an approximation of &radical;3
Give your answer in the form a/b where a and b are integers.
Trapezium Rule Figure 1 shows the finite region R bounded by the x-axis, the y-axis, the line π/2
the curve with equation
y = sec (1/2 x), 0 ≤ x ≤ π/2
The table shows corresponding values of x and y for y = sec(1/2 x)
(a) Complete the table above giving the missing value of y to 6 decimal places.
(b) Using the trapezium rule, with all of the values of y from the completed table, find an approximation for the area of R, giving your answer to 4 decimal places.
Region R is rotated through 2π radians about the x-axis.
(c) Use calculus to find the exact volume of the solid formed.
3(c) Volumes of Revolution
dy/dx for a parametric curve
4. A curve C has parametric equations
x = 2sin t, y = 1 – cos 2t, –π/2 ≤ t ≤ π/2
(a) Find dy/dx at the point where t = π/6
(b) Find a cartesian equation for C in the form
y = f(x), –k ≤ x ≤ k, stating the value of the constant k.
(c) Write down the range of f(x).
4 (b)(c) Parametric to Cartesian form
Integration by Substitution
5. (a) Use the substitution x = u2 , u > 0, to show that
(b) Hence show that
where a and b are integers to be determined.
5 (b)
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