Sorry about this extremely late scribe but I've been busy these last few days. What lies beneath the accumulation function? that is the question and the answer is not presents!
We were given F(t)=t as a function and have to find A(x) if A(x)= the derivative of F(t) on the interval 0 to x. We had to find the area under the F(t) and it turned out that A(x) was the parent function of F(t).
The second fundamental theorem of calculus states: if f is a continuous function on the interval [a,b] and an accumulation function is defined as the derivative of F(t) on the interval [a,x] then A'(x)= F(t).
He then gave us the question A(x) = derivative of sin(t) on the interval [1,x^2] and we have to find A'(x).
The answer is sin(x^2)*(2x)
Why?
You have to find the derivative of t on the intervals [1,x^2] then plug it in and then find the derivative of x.
Reason why, because Accumulation functions are Composite Functions.
Il try to get around to upgradeing my scribe with pics if anyone reminds me :)
Thats all
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