Question: Use the fact that 7 cos x - 4 sin x = (3/2)(cos x + sin x) + (11/2)(cos x - sin x) to find the exact value of (upper limit: 0.5?, lower limit: 0)?((7 cos x - 4 sin x)/(cos x + sin x)) dx.
Answer: 3/4?
I need help with the steps, thanks in advance!
Hello, margaritas!
Edit: I got your correction . . . I'll edit my solution.
Use the fact that:
to find the exact value of: .
Answer:. . . Right!
The function is: .
. .}{\cos x + \sin x} + \frac{\frac{11}{2}(\cos x - \sin x)}{\cos x + \sin x})
The integration is: .
. . For the second integral, let
. . then we have: .
Hence, we have: .
Evaluate: .![\left[\frac{3}{2}\left(\frac{\pi}{2}\right) + \frac{11}{2}\ln\left|\cos \frac{\pi}{2} + \sin \frac{\pi}{2}\right|\right] -](http://latex.codecogs.com/png.latex?\left[\frac{3}{2}\left(\frac{\pi}{2}\right) + \frac{11}{2}\ln\left|\cos \frac{\pi}{2} + \sin \frac{\pi}{2}\right|\right] -)
. .
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