What are the solutions to the equation
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Answer:
We can describe FOIL using the distributive property of multiplication. For real numbers x, y, and z the distributive property of multiplication states that
Now let , where v and w are real numbers.
Then
Here, we can again use the distributive property of multiplication to get
Hence, it follows that
This is the method of FOIL (first: xv, outside: xw, inside: yv, last: yw)
For example,
Suppose we let , so that
.
Also, recall the double angle identity for cosine:
So, we can rewrite and compute the integral using the substitution, as