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# 2011 Calculus AB free response #2 (c & d)

Second fundamental theorem of calculus application. Created by Sal Khan.

## Want to join the conversation?

• In this video Khan rounds at the hundreths place but I heard that for the AP Exam you need to round at the thousandths place. Is this true? • In a question like this, do I need to worry about the number of significant digits? The table of the temperatures of the tea gives us data with two significant digits. When we find the temperature of the biscuits to four significant digits and compare them to the temperature of the tea (which has two), aren't the two digits to the right of the decimal point meaningless? • When you integrate speed you get position, and when you differentiate speed you get acceleration. Is there a correlation with temperature? I can see when you differentiate it you get change in temperature over time. Is there any way to interpret the integral of a temperature function? • at when it's the integral of the derivative why isn't it the same as in part c? I thought it was the same thing where it's H'(10)'H'(0) in c so that part d is just B'(10) -B'(0) ? Why does he actually integrate it? • At around : Wherefore do you subtract 65.817247 from 100? • B(t) = integral B'(t) from 0 to t + y-intercept

It's said that when t = 0,
B(0) = 100

You can think of it as.. if x = 0, then y = 100
y-intercept is 100

B(0) = integral B'(t) from 0 to 0 + y-intercept
B(0) = 0 + y-intercept
B(0) = y-intercept
B(0) = 100

so when actually solving the problem where t = 10...

B(10) = integral B'(t) from 0 to 10 + 100
B(10) = -65.8172 + 100

does that help clarify?
• At , why do you divide by -.173? • Why didn't he just integrate b'(t) to get b(t) and use the initial condition of b(0)=100 to solve for the constant of integration and then just plug in t=10?   