Now, let's apply Wallis' formula to the given integral:
$$\int_0^{\frac{\pi}{2}} \sin^8(x) \cos^1(x) dx$$
Here, we have n = 8 and m = 1. So, we can plug these values into Wallis' formula:
$$\frac{(8-1)!!(1-1)!!}{(8+1)!!} \cdot \frac{\pi}{2}$$
Now, let's
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