Question 1

Express the area of the given region as a definite integral. Do not evaluate.

Accepted Answer

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Question 2

Find the area of the shaded region:

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Question 3

Find the area of the region bounded by $y = x ( x - 1 ) ( x - 2 ) \text { and the } x - \text { axis. }$

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Question 4

Find the area of the shaded region:

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Question 5

A stone is thrown straight up from the top of a tower that is 80 ft tall with initial velocity 64 ft/s. What is the total distance traveled by the stone when it hits the ground?

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Question 6

Find the area of the shaded region:

Accepted Answer

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Question 7

Find the area of the region bounded by $y = x ^ { 3 } - 6 x \text { and } y = - 2 x$

Accepted Answer

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Question 8

Express the area of the given region as a definite integral. Do not evaluate.

Accepted Answer

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Question 9

A particle is moving in a straight line and its velocity is given by $v ( t ) = 3 t ^ { 2 } - 12 t + 9,$ where t is measure in seconds and v in meters per second. Find the distance traveled by the particle during the time interval $[ 0,5 ]$ .

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Quiz 6: Applications of Integration

Express the area of the given region as a definite integral. Do not evaluate.

Find the area of the shaded region:

Find the area of the region bounded by y=x(x−1)(x−2) and the x− axis. y = x ( x - 1 ) ( x - 2 ) \text { and the } x - \text { axis. }y=x(x−1)(x−2) and the x− axis.

Find the area of the shaded region:

A stone is thrown straight up from the top of a tower that is 80 ft tall with initial velocity 64 ft/s. What is the total distance traveled by the stone when it hits the ground?

Find the area of the shaded region:

Find the area of the region bounded by y=x3−6x and y=−2xy = x ^ { 3 } - 6 x \text { and } y = - 2 xy=x3−6x and y=−2x

Express the area of the given region as a definite integral. Do not evaluate.

A particle is moving in a straight line and its velocity is given by v(t)=3t2−12t+9,v ( t ) = 3 t ^ { 2 } - 12 t + 9,v(t)=3t2−12t+9, where t is measure in seconds and v in meters per second. Find the distance traveled by the particle during the time interval [0,5][ 0,5 ][0,5] .

Find the area of the region bounded by $y = x ( x - 1 ) ( x - 2 ) \text { and the } x - \text { axis. }$

Find the area of the region bounded by $y = x ^ { 3 } - 6 x \text { and } y = - 2 x$

A particle is moving in a straight line and its velocity is given by $v ( t ) = 3 t ^ { 2 } - 12 t + 9,$ where t is measure in seconds and v in meters per second. Find the distance traveled by the particle during the time interval $[ 0,5 ]$ .