Question 1

Express the area of the shaded region in terms of an integral (or integrals).Do not evaluate the expression:

Accepted Answer

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Question 2

The exact area of the region bounded by the graphs of y = x,y =  ,y = 2,and y = 3 is

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Question 3

Find the area of the region bounded by the given equations:
y =  
+ 6x + 10 and y = x + 6

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Question 4

Find the area of the region bounded by the curves y =  
and y = x + 2 from x = 1 to x = 2.

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Question 5

The exact area of the region bounded by the graphs of y =  - 5 and y = 2x + 3 is

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Question 6

The demand equation for a certain product is p = 30 - 0.1q,where p is the price per unit (in dollars)for q units.If its supply equation is p = 0.15q + 5,find the consumers' surplus and the producers' surplus when market equilibrium has been established.

Accepted Answer

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Question 7

The exact area of the region bounded by the graphs of y = x and y =  is

Accepted Answer

The answer of The exact area of the region bounded...

Question 8

The demand equation for a certain product is p = 200 -  
,where p is the price per unit (in dollars)for q units.If its supply equation is p = 6q + 160,find the consumers' surplus and the producers' surplus when market equilibrium has been established.

Accepted Answer

The answer of The demand equation for a certain product...

Question 9

Find the area of the region bounded by the curves y =  
- 4 and y = 2x +  
from x = 1 to x = 2.

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Question 10

Find the exact area of the region bounded by the graphs of y = 9 -  
and y = 5 - 3x.Also sketch the region.

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Question 11

Find the exact area of the region bounded by the graphs of y = -x,y = 2x,y = 1,and y = 2.Also sketch the region.

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Question 12

Find the area of the region enclosed by the graphs of y =  
-  
and y = 2x.

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Question 13

The demand equation for a certain product is p = 400 - 2q,where p is the price per unit (in dollars)for q units.If its supply equation is p = q + 100,then the consumers' surplus when market equilibrium is established is

Accepted Answer

To find the market equilibrium, we set the demand equation equal to the supply equation:
400 - 2q = q + 100
3q = 300
q = 100
Then we can find the equilibrium price by plugging q = 100 into either equation:
p = 400 - 2(100) = 200
p = 100 + 100 = 200
So the equilibrium price is $200 per unit.
To find the consumers' surplus, we need to integrate the demand equation from 0 to 100 units:
∫(400 - 2q) dq from 0 to 100
= [(400q - q^2)/2] from 0 to 100
= [20000 - 10000]/2
= $10,000
Therefore, the consumers' surplus when market equilibrium is established is $10,000.

Question 14

Find the exact area of the region bounded by the graphs of x =  
and x - y - 2 = 0.Also sketch the region.

Accepted Answer

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Question 15

Express the area of the shaded region in terms of an integral (or integrals).Do not evaluate the expression:

Accepted Answer

The answer of Express the area of the shaded region...

Question 16

Find the exact area of the region bounded by y = f(x)= 8 - 2x -  
and the x-axis.

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Question 17

Find the exact area of the region bounded by the graphs of y = 8 - 2x -  
and y = 3x + 2.Also sketch the region.

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Question 18

Find the area of the region bounded by the given equations:
y =  
- x - 9 and y = -  
+ 3x + 7

Accepted Answer

The answer of Find the area of the region bounded...

Question 19

Express the area of the shaded region in terms of an integral (or integrals).Do not evaluate the expression:

Accepted Answer

The answer of Express the area of the shaded region...

Question 20

Find the exact area of the region bounded by y = f(x)=  
,x = -2,x = 2,and the x-axis.

Accepted Answer

The answer of Find the exact area of the region...

Quiz 16: Methods and Applications of Integration

Express the area of the shaded region in terms of an integral (or integrals).Do not evaluate the expression:

The exact area of the region bounded by the graphs of y = x,y = ,y = 2,and y = 3 is

Find the area of the region bounded by the given equations: y = + 6x + 10 and y = x + 6

Find the area of the region bounded by the curves y = and y = x + 2 from x = 1 to x = 2.

The exact area of the region bounded by the graphs of y = - 5 and y = 2x + 3 is

The demand equation for a certain product is p = 30 - 0.1q,where p is the price per unit (in dollars)for q units.If its supply equation is p = 0.15q + 5,find the consumers' surplus and the producers' surplus when market equilibrium has been established.

The exact area of the region bounded by the graphs of y = x and y = is

The demand equation for a certain product is p = 200 - ,where p is the price per unit (in dollars)for q units.If its supply equation is p = 6q + 160,find the consumers' surplus and the producers' surplus when market equilibrium has been established.

Find the area of the region bounded by the curves y = - 4 and y = 2x + from x = 1 to x = 2.

Find the exact area of the region bounded by the graphs of y = 9 - and y = 5 - 3x.Also sketch the region.

Find the exact area of the region bounded by the graphs of y = -x,y = 2x,y = 1,and y = 2.Also sketch the region.

Find the area of the region enclosed by the graphs of y = - and y = 2x.

The demand equation for a certain product is p = 400 - 2q,where p is the price per unit (in dollars) for q units.If its supply equation is p = q + 100,then the consumers' surplus when market equilibrium is established is

Find the exact area of the region bounded by the graphs of x = and x - y - 2 = 0.Also sketch the region.

Express the area of the shaded region in terms of an integral (or integrals).Do not evaluate the expression:

Find the exact area of the region bounded by y = f(x)= 8 - 2x - and the x-axis.

Find the exact area of the region bounded by the graphs of y = 8 - 2x - and y = 3x + 2.Also sketch the region.

Find the area of the region bounded by the given equations: y = - x - 9 and y = - + 3x + 7

Express the area of the shaded region in terms of an integral (or integrals).Do not evaluate the expression:

Find the exact area of the region bounded by y = f(x)= ,x = -2,x = 2,and the x-axis.