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17. (a) Express \(\sin x - \cos x^2\) in the form \(p + q \sin r x\) where \(p\), \(q\) and \(r\) are integers - Scottish Highers Maths - Question 17 - 2019
Question 17
17. (a) Express \(\sin x - \cos x^2\) in the form \(p + q \sin r x\) where \(p\), \(q\) and \(r\) are integers. (b) Hence, find \(\int (\sin x - \cos x^2) \, dx\).
Worked Solution & Example Answer:17. (a) Express \(\sin x - \cos x^2\) in the form \(p + q \sin r x\) where \(p\), \(q\) and \(r\) are integers - Scottish Highers Maths - Question 17 - 2019
Step 1
Hence, find \(\int (\sin x - \cos x^2) \, dx\)
Answer
Using the result from part (a), we need to integrate (\sin x - \cos x^2). This gives:
[ \int (\sin x - \cos x^2) , dx = -\cos x + \int \cos x^2 , dx + C ]
However, the integral of (\cos x^2) does not have a simple closed form. Therefore, we leave our answer in this form:
[ = -\cos x + C ]