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?

Question

anonymous · Answer

study

anonymous · Answer

Be more specific.

anonymous · Answer

can somone help me do a problem

anonymous · Answer

kinda coach me through it

anonymous · Answer

attachment

anonymous · Answer

how would we begin this problem?

jim_thompson5910 · Answer

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

jim_thompson5910 · Answer

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.

anonymous · Answer

attachment

jim_thompson5910 · Answer

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