8.2 (Applications to Geometry)

Question 1

How do you find the area between two curves f(x) and g(x)?

Answer 1

integrate the difference of the two functions over the interval [a,b] where you subtract the lower curve from the upper curve

Question 2

what is the formula to find the area between two curves f(x) and g(x)?

Answer 2

the intergral from a to b of the absolute value of f(x) minus g(x) dx

Question 3

What is the formula for the volume of a solid of revolution using the Disk Method?

Answer 3

V=the integral from a to b of pi times f(x) squared dx

Question 4

What is the formula for the volume of a solid of revolution using the Washer Method?

Answer 4

V= ∫a to b π ( [ R(x) ]^2−[ r(x) ]^2 )dx

Question 4

How do you calculate the arc length of a curve y=f(x) from x=a to x=b?

Answer 4

L=∫a to b square root of 1+[f′(x)]^2dx

Question 5

What is the formula to find the surface area of a solid of revolution around the x-axis?

Answer 5

S= ∫a to b of 2πf(x) square root of 1+[f′(x)]^2dx

Question 6

How do you find the centroid (center of mass) of a region bounded by y=f(x) and y=g(x) for the x coordinate?

Answer 6

xˉ= 1/A ∫a to b x[f(x)−g(x)]dx

Question 6

How do you find the centroid (center of mass) of a region bounded by y=f(x) and y=g(x) for the y coordinate?

Answer 6

yˉ=1/A ∫a to b (f(x)+g(x)/2) [f(x)−g(x)]dx