Calculus 1: Applications of Integration
Find the area between the two curves and
Find the area between the curves and
Compute the area between and and the interval
Compute the area of the region bounded by the curves and
Find the average value on of
What is the average value of the function on
Find the average value of the function on
Determine the volume of the solid generated by rotating the function about the x-axis on
Determine the volume of the solid generated by rotating the function about the y-axis on
Use the shell method to determine the volume formed by the bounded region rotated about the x-axis.
, ,
Use the shell method to determine the volume of the solid formed by rotating the region about the y axis.
, ,
Let R be the region enclosed by the graph of and the horizontal line y = 4, as shown in the figure above.
A. Find the volume of the solid generated when R is rotated about the horizontal line y = -2
B. Region R is the base of a solid. For this solid, each cross section perpendicular to the x-axis is an isosceles right triangle with a leg in R. Find the volume of the solid.
C. The vertical line x = k divides R into two regions with equal areas. Write, but do not solve, an equation involving integral expressions whose solution gives the value k.
Use the disk method to find the volume of the solid of rotation by rotating the bounded area around the y-axis
, ,