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1.a) [5 marks] Solve the integral

1

dx. Use an inverse trigonometric substitut

tion of the form x = B tan (0) for some BER.

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1.b) [2 marks] Evaluate the improper integral

A

dxx.

-DO

1.c) [1 mark] Substitute A =

VUn TO

and v = 3 into your work from Question 1.b) to

confirm that:

r(7+1)

u+1

2

2

dt

=1

-OC

In other words, confirm that p(t) satisfies the definition of a probability density function.Math