diff --git a/education/calculus/precalculus/Composing Functions.md b/education/calculus/precalculus/Composing Functions.md deleted file mode 100644 index ca53f70..0000000 --- a/education/calculus/precalculus/Composing Functions.md +++ /dev/null @@ -1,3 +0,0 @@ -- To compose a function is to create a new function from multiple smaller functions. -- They can be solved from the inside out -- \ No newline at end of file diff --git a/education/math/MATH1220 (calc II)/Integration with Trig Identities.md b/education/math/MATH1220 (calc II)/Integration with Trig Identities.md index 6bbe4e7..332135a 100644 --- a/education/math/MATH1220 (calc II)/Integration with Trig Identities.md +++ b/education/math/MATH1220 (calc II)/Integration with Trig Identities.md @@ -49,5 +49,10 @@ $$ = 3\int\frac{1}{4(\sec^2\theta)}(2\sec^2\theta)d\theta$$ $$ 3\int\frac{2}{4}d\theta = \frac{3}{2} \theta + C$$ 6. At this point, we want to determine what $\theta$ is equal to relative to $x$. 1. Look back to step 2 we defined $x = 2\tan\theta$ - 2. Moving $2$ to the other side to, -$$ $$ \ No newline at end of file + 2. Moving $2$ to the other side, we get $\frac{x}{2} = \tan\theta$ + 3. Because we defined bounds for our definition of $\theta$, we can take advantage of $\arctan$, therefore: +$$ \theta = \arctan(\frac{x}{2}) $$ +7. Rewriting the equation with $\theta$ in terms of x, we get: +$$ \frac{3}{2}\arctan(\frac{x}{2}) + C$$ +This means that: +$$ \int\frac{3}{4+x^2}dx = \frac{3}{2}\arctan(\frac{x}{2}) + C $$ \ No newline at end of file