So this week we got back into a little new stuff, which was kind of easy. We learned how to integrate properly and find the area of a section on a graph. For this blog, I'm going to review about natural logs and some integration.
The derivative of a natural log is 1/f(x) x the derivative of the bottom
ex: lnx^5 = 1/x^5 x 5x4 = 5x^4/x5 = 5/x
ex: ln2x = 1/2x x 2 = 2/2x = 1/x
ex: lnx^3-2x+3 = 1/x^3-2x+3 x 3x^2-2 = 3x^2-2/x^3-2x+3
Integration, in simpler terms, is taking the "backwards derivative" wherein you're given f'(x) and you're looking for f(x).
ex: f'(x) = x^2
add one to the exponent then multiply x by its reciprocal and add the variable C, because we are not sure if there is a constant in the original function.
solution: f(x)=1/3x^3 + C
ex: f'(x)=x^2 + 4x + 3
1/3/x^3 + 2x^2 + 3x + C
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