Question

In part (d) of the first problem, the one about W(t), why do they add 71 to the integral? https://secure-media.collegeboard.org/ap-student/pdf/calculus-ab/ap-2012-calculus-ab-scoring-guidelines.pdf

Answer 1

The integral represents the increase in \(t\) from 20 to 25, but it's just that; the value of the integral doesn't tell you the water's overall temperature, which is why you need to include the temp at \(t=20\).

Answer 2

If you've had some experience with differential equations, you can also think of it in terms of an initial value problem. If \(W(20)=71\) and \(W'(t)=\cdots\), then you would integrate \(W'(t)\) to get \(W(t)+C\) and plug in \(W(20)=71\) to solve for \(C\).

Answer 3

what does W(t) + c represent?

Answer 4

does W(t) + c represent the temperature at any time, or a certain time?