MATH105 April 2011
• Q1 (a) • Q1 (b) • Q2 • Q3 • Q4 • Q5 (a) • Q5 (b) • Q5 (c) • Q6 • Q7 • Q8 (a) • Q8 (b) • Q8 (c) • Q9 (a) • Q9 (b) • Q9 (c) • Q9 (d) • Q9 (e) • Q9 (f) • Q9 (g) •
Question 01 (b)
Find the value of the following definite integral:
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The power of is odd. Is there a strategy that would be useful?
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We will first compute the indefinite integral and evaluate our results at the boundaries of the integral to get the final result.
The first step is to split a -factor from in the integrand:
Now we use the trigonometric Pythagoras to write and arrive at
The next step is to use the substitution rule with . This implies or equivalently . Substituting this into the integral yields
Rewriting this integral in terms of by using the substitution equation results in
Therefore, we can compute our original definite integral as follows:
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