Question

I understand the first part of the fundemantal threom of calculus, but the second part is killing, anybody got any tips or tricks to understand it?

Answer 1

study

Answer 2

Be more specific.

Answer 3

can somone help me do a problem

Answer 4

kinda coach me through it

Answer 5

how would we begin this problem?

Answer 6

The second part of the FTC (fundamental theorem of calculus) says that

\[\int_{a}^{b} f(x)dx = g(b)-g(a)\]

where g(x) is the antiderivative of f(x)


In this case,

\[\int (t+2)dt=\frac{1}{2}t^2+2t+C\]

So \[\int_{0}^{x} (t+2)dt=(\frac{1}{2}x^2+2x+C)-(\frac{1}{2}(0)^2+2(0)+C)=\frac{1}{2}x^2+2x\]

Answer 7

I'm just realizing that some books present the FTC in different order. Let me know if this is the portion you're referring to.

Answer 8

Assuming you mean F(x) in the attachment, you have the right answer.