AP Calculus AB - Unit 8 Progress Check - MCQs (parts A & B)

[@peaceofwestphalia]

U R THE BEST

[@user-pv4hn5eq3k]

Thank you Reid omg you carried my whole math class this semester

[@liammendi]

Why do you use pir^2 for the cross sections instead of just f(x)-g(x) by itself on question 3 and 4

[@reidsinclair1103]

When you rotate an area about a line, cross sections are always circles. Since the area of a circle is pir^2, and the functions are the radius(sometimes plus or minus a constant), you need to integrate pi[f(x)]^2 or pi[f(y)]^2 to find the volume. If there is a gap between the area that is being rotated and the line of rotation, the solid will have a hollowed out portion, which you can account for by subtracting that inside volume

[@naffgirl8338]

Thank you so much!

[@lizmorgievich8733]

for question 4 on part b, why do you use the bounds 0 to A, and not something in terms of x?

[@reidsinclair1103]

Hi. That value of A(about 3.39) is an x-value. And any time that you revolve around the x-axis, or a line parallel to the x-axis, your limits and integrand need to be in terms of x

[@foshio1598]

REIDDDDDDD YOURE THE BEST

[@AryanGupta-sr3sh]

At 49:53 how do you know which order to put the equations in for the integral

[@reidsinclair1103]

You’ll do (top - bottom) if your functions are in terms of x “y=f(x)”. You’ll do (right - left) if your functions are in terms of y “x=f(y)”. Sometimes you can do either way, sometimes only one way will be possible. It depends on 2 things: 1) which variable you can solve your function in terms of (some functions can only be solved in terms of a certain variable, at least in this class) & 2) it might be easier, or only possible, to do one way (top-bottom or right-left) depending on if the one function is above/below the other function throughout the entire interval that the area spans over, or if one function is to the right/left of the other function throughout the interval

[@danimartin4934]

where did you get radical 3/4 in area of triangle

[@pharo.3074]

the integrand defined by an equilateral triangle is represented by A=sqrt3/4 b^2