Deck 8: Further Applications of Integration

Question 1

Find the area of the surface obtained by rotating the curve about the -axis.

Answer 1

Question 2

Answer 2

Question 3

Answer 3

Question 4

Question 5

For a given commodity and pure competition, the number of units produced and the price per unit
are determined as the coordinates of the point of intersection of the supply and demand curves.
Given the demand curve

Question 6

Question 7

Find the area of the surface obtained by revolving the given curve about the y-axis.

Question 8

Find the centroid of the region shown, not by integration, but by locating the centroids of the
rectangles and triangles and using additivity of moments.

Question 9

Question 10

Question 11

Let the function whose graph is shown be a probability density function.Calculate the mean.

Question 12

Question 13

Find the centroid of the region shown in the figure.

Question 14

Find the center of mass of the lamina of the region shown if the density of the circular lamina is six times that
of the rectangular lamina.

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20

Question 21

Question 22

Question 23

Question 24

Find the centroid of the region bounded by the given curves.

Question 25

Question 26

Question 27

Question 28

Question 29

Question 30

Question 31

Find the centroid of the region bounded by the given curves.

Question 32

Question 33

Question 34

Find the centroid of the region bounded by the graphs of the given equations.

Question 35

Question 36

Question 37

Question 38

Question 39

Question 40

Question 41

Question 42

Question 43

The marginal revenue from producing x units of a certain product is

Question 44

Question 45

Question 46

Find the length of the curve.

Question 47

Question 48

Question 49

Question 50

Question 51

Question 52

Question 53

Question 54

Question 55

Question 56

Question 57

Question 58

Question 59