Question

can someone just explain what to do on these two please?

ap calc bc

**postin pic

Answer 1

Well, its giving you the integral of f'(x), which would just be f(x). So whatever f'(x)is, when you integrate you, youll be doing f(4)-f(1). Well, it already said f(1) = 12 and f(4)-f(1) = 17.

Answer 2

oh awk I could of thought that one out. Ok I get that one now that you point it out (thank you) lol
ok and for the second one would i do something like this: \[\int\limits_{0}^{\pi} (1+cosx)dx \]

Answer 3

then i'd have to subtract something to get only the shaded region..right?

Answer 4

Right, for the second part. Integrating a function gives you area under a curve, but we want the area above the curve and bounded by y = 2. So if you simply integrated y = 2 from 0 to pi, youd get the whole entire box. From there, we can get the specific shaded region by subtraction the area of 1 + cosx. so we have
\[\int\limits_{}^{}2-(1+cosx)dx\]

Answer 5

oh ok i'm kind of following. I understand that integrating y=2 get's u the entire box and it makes sense that u're going to subtract 2-(1 + cosx) but would the interval still be from 0 to pi?

Answer 6

Absolutely. The interval is the bounds for the entire problem, no matter what we want to find. Those bounds wont ever change unless it explicitly tells us theyre different. The only reason you would choose different intervals is if you had to do separate integrations within the larger interval or if you had to switch to the other axis for some reason. But the boundaries are always the boundaries.

Answer 7

ok I was hoping i had the right idea! haha thank you sooo much! Really appreciate you clarifying my questions(:

Answer 8

Np :3