MATHEMATICS ASSIGNMENT 2
Provide solution to the following questions:
Question 1. Evaluate the following:
Solution
Integrating by parts, we apply the formula ∫ udv = uv  ∫ vdu such that u = x and dv = sin (3x).
Thus x(
cos (3x))  ∫ 
cos (3x) dx –
 ∫
. However, since 1 is a constant
with respect to x, we integrate
with respect to x to get  ∫

Multiplying 1 by 1 we get 1, thus
Multiply
by 1, to get
Thus
∫
is a constant with respect to x in both equations, thus, the integral of
with respect to x is
.
Let u = 3x, and du = 3dx, thus
. The equation can then be rewritten using u and du
such that,

Since