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The following videos will give you the worked solutions and answers for the Edexcel GCE Core Mathematics C4 Advanced June 2013. The questions are given here.

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C4 Edexcel Core Mathematics June 2013 Question 1

Integration by Parts

1. (a) Find ∫x^{2} e^{x} 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.

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 = u^{2}
, u > 0, to show that

(b) Hence show that

where a and b are integers to be determined.

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