Exam 16: Methods and Applications of Integration

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Use the table below to determine Use the table below to determine    dx.Indicate the formula number employed. I.    + C II.    + C III.        + C IV.    + C dx.Indicate the formula number employed. I. Use the table below to determine    dx.Indicate the formula number employed. I.    + C II.    + C III.        + C IV.    + C + C II. Use the table below to determine    dx.Indicate the formula number employed. I.    + C II.    + C III.        + C IV.    + C + C III. Use the table below to determine    dx.Indicate the formula number employed. I.    + C II.    + C III.        + C IV.    + C Use the table below to determine    dx.Indicate the formula number employed. I.    + C II.    + C III.        + C IV.    + C + C IV. Use the table below to determine    dx.Indicate the formula number employed. I.    + C II.    + C III.        + C IV.    + C + C

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If If   = 3   Y and y > 0,y(0)= 4,then y = = 3 If   = 3   Y and y > 0,y(0)= 4,then y = Y and y > 0,y(0)= 4,then y =

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The exact area of the region bounded by the graphs of y = The exact area of the region bounded by the graphs of y =   - 4,and the x-axis from x = 0 to x = 4 is - 4,and the x-axis from x = 0 to x = 4 is

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Use the formula Use the formula    = ln    + C to find  = ln Use the formula    = ln    + C to find  + C to find Use the formula    = ln    + C to find

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The average value of f(x)= The average value of f(x)=   + 1 over the interval   Is + 1 over the interval The average value of f(x)=   + 1 over the interval   Is Is

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

(Short Answer)
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Find the area between the graph of y = f(x)= Find the area between the graph of y = f(x)=    ,and the x-axis on the interval    .Use your graphing calculator to see a graph of this area. ,and the x-axis on the interval Find the area between the graph of y = f(x)=    ,and the x-axis on the interval    .Use your graphing calculator to see a graph of this area. .Use your graphing calculator to see a graph of this area.

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Use Simpson's rule with n = 4 to find an approximate value of Use Simpson's rule with n = 4 to find an approximate value of

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An oil tanker is losing oil at a rate of R'(t)= An oil tanker is losing oil at a rate of R'(t)=    where t is the time in minutes and R(t)is the radius of the oil slick in feet.Use n = 6 and Simpson's rule to approximate    the size of the radius after 5 seconds. where t is the time in minutes and R(t)is the radius of the oil slick in feet.Use n = 6 and Simpson's rule to approximate An oil tanker is losing oil at a rate of R'(t)=    where t is the time in minutes and R(t)is the radius of the oil slick in feet.Use n = 6 and Simpson's rule to approximate    the size of the radius after 5 seconds. the size of the radius after 5 seconds.

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Solve the differential equation y' = Solve the differential equation y' =    if y > 0. if y > 0.

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If 65% of the initial amount of a radioactive sample has decayed after 5 hours,find the decay constant λ and the half life of the element.

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

(Multiple Choice)
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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.

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The velocity of an object is given by V(t)= The velocity of an object is given by V(t)=    ,where t is the time in seconds and V(t)is the speed in feet/sec.Use n = 6 and the trapezoidal rule to approximate    the distance moved over the interval    . ,where t is the time in seconds and V(t)is the speed in feet/sec.Use n = 6 and the trapezoidal rule to approximate The velocity of an object is given by V(t)=    ,where t is the time in seconds and V(t)is the speed in feet/sec.Use n = 6 and the trapezoidal rule to approximate    the distance moved over the interval    . the distance moved over the interval The velocity of an object is given by V(t)=    ,where t is the time in seconds and V(t)is the speed in feet/sec.Use n = 6 and the trapezoidal rule to approximate    the distance moved over the interval    . .

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Solve the differential equation Solve the differential equation    =    y if y > 0 and y = 2 when x = 0. = Solve the differential equation    =    y if y > 0 and y = 2 when x = 0. y if y > 0 and y = 2 when x = 0.

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Use the table below to determine Use the table below to determine    dx.Indicate the formula number employed. I.    + C II.    + C III.        + C IV.    + C dx.Indicate the formula number employed. I. Use the table below to determine    dx.Indicate the formula number employed. I.    + C II.    + C III.        + C IV.    + C + C II. Use the table below to determine    dx.Indicate the formula number employed. I.    + C II.    + C III.        + C IV.    + C + C III. Use the table below to determine    dx.Indicate the formula number employed. I.    + C II.    + C III.        + C IV.    + C Use the table below to determine    dx.Indicate the formula number employed. I.    + C II.    + C III.        + C IV.    + C + C IV. Use the table below to determine    dx.Indicate the formula number employed. I.    + C II.    + C III.        + C IV.    + C + C

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

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Use the table below to determine Use the table below to determine    dx.Indicate the formula number employed. I.    + C II.    + C III.        + C IV.    + C dx.Indicate the formula number employed. I. Use the table below to determine    dx.Indicate the formula number employed. I.    + C II.    + C III.        + C IV.    + C + C II. Use the table below to determine    dx.Indicate the formula number employed. I.    + C II.    + C III.        + C IV.    + C + C III. Use the table below to determine    dx.Indicate the formula number employed. I.    + C II.    + C III.        + C IV.    + C Use the table below to determine    dx.Indicate the formula number employed. I.    + C II.    + C III.        + C IV.    + C + C IV. Use the table below to determine    dx.Indicate the formula number employed. I.    + C II.    + C III.        + C IV.    + C + C

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Use the tables to find: Use the tables to find:

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The demand equation for a certain product is p = 25 - 0.005q,where p is the price per unit (in dollars)for q units.If its supply equation is p = 1 + 0.03q,then the consumers' surplus when market equilibrium is established is

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