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**Who Wants to Be a Millionaire?**

Template by Bill Arcuri, WCSD

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**Anti- derivatives _________________________ _____________________**

Click the appropriate dollar amount at right to proceed to the question Template by Bill Arcuri, WCSD

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Phone A Friend “OK Contestant…Please select a friend to help you with this one. You have thirty seconds to discuss your options…” Return to the Question Template by Bill Arcuri, WCSD

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Ask the Audience “Audience, we need your help on this one…in a moment, we’ll ask you to indicate, by show of hands, your choice for the correct answer…” Return to the Question Template by Bill Arcuri, WCSD

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50/50 Fifty - Fifty You’ve asked that two of the wrong answers be eliminated, leaving you with one wrong answer plus the correct one. Return to the Question Template by Bill Arcuri, WCSD

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**Proceed to Next Question**

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**Question #1... 𝑑 𝑑𝑥 0 3𝑥 cos 𝑡 𝑑𝑡 50/50 A B C D 𝒔𝒊𝒏 𝟑𝒙 −𝟑 𝒔𝒊𝒏 𝟑𝒙**

𝟑 𝒄𝒐𝒔 𝟑𝒙 A B 𝒄𝒐𝒔 𝟑𝒙 𝒔𝒊𝒏 𝟑𝒙 C D Template by Bill Arcuri, WCSD

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**Question #2... 𝑥−18 (𝑥+3)(𝑥−4) 𝑑𝑥= 50/50 A B C D 𝟓𝒅𝒙 (𝒙+𝟑)(𝒙−𝟒)**

𝟑𝒅𝒙 𝒙+𝟑 + 𝟐𝒅𝒙 𝒙−𝟒 A B 𝟏𝟓 𝒅𝒙 𝒙+𝟑 − 𝟏𝟒 𝒅𝒙 𝒙−𝟒 𝟑𝒅𝒙 𝒙+𝟑 − 𝟐𝒅𝒙 𝒙−𝟒 C D Template by Bill Arcuri, WCSD

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**Question #3... Using rectangles to estimate the area under a curve from x = a to x = b is**

50/50 Trapezoid Sum Triangle Sum A B Riemann Sum Some Sum C D Template by Bill Arcuri, WCSD

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**Question #4... The average value of **

𝑓 𝑥 =𝑥 ln 𝑥 on the interval [1,e] is 50/50 𝒆 𝟐 +𝟏 𝟒(𝒆−𝟏) 𝒆 𝟐 −𝟏 𝟒(𝒆−𝟏) A B 𝒆 𝟐 +𝟏 𝟒(𝒆+𝟏) 𝒆−𝟏 𝟒(𝒆+𝟏) C D Template by Bill Arcuri, WCSD

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**Question #5... 2 𝑒+1 4 𝑥−1 𝑑𝑥= 50/50 A B C D 4e 4 -4e**

-4e C D Template by Bill Arcuri, WCSD

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Question #6... Use the table below to find a right Riemann approximation with 4 subintervals for 𝑓 𝑥 𝑑𝑥 x 3 5 8 9 12 f (x) 10 6 50/50 65 67 A B 87.75 69 C D Template by Bill Arcuri, WCSD

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**Question #7... 𝒙 𝟐 𝒄𝒐𝒔( 𝒙 𝟑 ) 𝒅𝒙 50/50 A B C D − 𝟏 𝟑 𝒔𝒊𝒏 𝒙 𝟑 +𝑪**

− 𝟏 𝟑 𝒔𝒊𝒏 𝒙 𝟑 +𝑪 𝟏 𝟑 𝒔𝒊𝒏 𝒙 𝟑 +𝑪 A B − 𝒙 𝟑 𝟑 𝒔𝒊𝒏 𝒙 𝟑 +𝑪 𝒙 𝟑 𝟑 𝒔𝒊𝒏 𝒙 𝟑 +𝑪 C D Template by Bill Arcuri, WCSD

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Question #8... Trapezoidal sum overapproximates 𝑎 𝑏 𝑓 𝑥 𝑑𝑥 and left Riemann sum underapproximates 𝑎 𝑏 𝑓 𝑥 𝑑𝑥 . Which of the following describes 𝑓(𝑥)? 50/50 f(x) is inc and concave down f(x) is inc and concave up A B f(x) is dec and concave down f(x) is dec and concave up C D Template by Bill Arcuri, WCSD

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**Question #9... 𝒙 𝒔𝒊𝒏 𝟐𝒙 𝒅𝒙 = 50/50 A B C D 𝒙 𝟐 𝒄𝒐𝒔 𝟐𝒙 + 𝟏 𝟒 𝒔𝒊𝒏 𝟐𝒙 +𝑪**

− 𝒙 𝟐 𝒄𝒐𝒔 𝟐𝒙 + 𝟏 𝟐 𝒔𝒊𝒏 𝟐𝒙 +𝑪 A B −𝒙 𝒄𝒐𝒔 𝟐𝒙 +𝒔𝒊𝒏 𝟐𝒙 +𝑪 − 𝒙 𝟐 𝒄𝒐𝒔 𝟐𝒙 + 𝟏 𝟒 𝒔𝒊𝒏 𝟐𝒙 +𝑪 C D Template by Bill Arcuri, WCSD

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**Question #10... If 𝑓 𝑥 = 0 𝑥+1 3 𝑡 2 −1 𝑑𝑡, then 𝑓 ′ 2 =**

50/50 2 A B 𝟑 𝟏𝟓 𝟑 −𝟗 C D Template by Bill Arcuri, WCSD

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**Question #11... 𝟑𝒙+𝟏 𝟓 𝒅𝒙= 50/50 A B C D 𝟑𝒙+𝟏 𝟔 𝟏𝟖 +𝑪 𝟑𝒙+𝟏 𝟔 𝟔 +𝑪**

𝟑𝒙+𝟏 𝟔 𝟏𝟖 +𝑪 𝟑𝒙+𝟏 𝟔 𝟔 +𝑪 A B 𝟑𝒙+𝟏 𝟔 𝟐 +𝑪 𝟑 𝒙 𝟐 𝟐 +𝒙 𝟔 +𝑪 C D Template by Bill Arcuri, WCSD

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**Question #12... 𝟐𝒙 𝒙+𝟐 𝒙+𝟏 𝒅𝒙= 50/50 A B C D 𝒍𝒏 𝒙+𝟐 +𝒍𝒏 𝒙+𝟏 +𝑪**

𝒍𝒏 𝒙+𝟐 +𝒍𝒏 𝒙+𝟏 −𝟑𝒙+𝑪 A B 𝟐𝒍𝒏 𝒙 + 𝟐 𝟑 𝒙+ 𝟏 𝟐 𝒙 𝟐 +𝑪 4𝒍𝒏 𝒙+𝟐 −𝟐 𝒍𝒏 𝒙+𝟏 +𝑪 C D Template by Bill Arcuri, WCSD

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**Question #13... 𝒆 𝒙 𝒄𝒐𝒔𝒙 𝒅𝒙= 50/50 A B C D 𝒆 𝒙 𝟐 𝒔𝒊𝒏 𝒙+𝒄𝒐𝒔 𝒙 +𝑪**

𝒆 𝒙 𝟐 𝒔𝒊𝒏 𝒙+𝒄𝒐𝒔 𝒙 +𝑪 𝒆 𝒙 𝟐 𝒄𝒐𝒔 𝒙−𝒔𝒊𝒏 𝒙 +𝑪 A B 𝒆 𝒙 𝟐 𝒔𝒊𝒏 𝒙−𝒄𝒐𝒔 𝒙 +𝑪 𝟐 𝒆 𝒙 (𝒔𝒊𝒏 𝒙+𝒄𝒐𝒔 𝒙)+𝑪 C D Template by Bill Arcuri, WCSD

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Question #14... The velocity, in ft/sec, of a particle moving along the x-axis is given by the function 𝑣 𝑡 = 𝑒 𝑡 +𝑡 𝑒 𝑡 . What is the average velocity of the particle from time t = 0 to time t = 3? 50/50 ft/sec ft/sec A B ft/sec ft/sec C D Template by Bill Arcuri, WCSD

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**Question #15. 𝑔 𝑥 = 0 𝑥 sin 𝑡 2 𝑑𝑡 for −1≤𝑡≤3**

Question #15... 𝑔 𝑥 = 0 𝑥 sin 𝑡 2 𝑑𝑡 for −1≤𝑡≤3. On which of the following intervals is g decreasing? 50/50 𝟏.𝟕𝟕𝟐≤𝒙≤𝟐.𝟓𝟎𝟕 𝟐.𝟖𝟎𝟐≤𝒙≤𝟑 A B 𝟎≤𝒙≤𝟏.𝟕𝟕𝟐 −𝟏≤𝒙≤𝟎 C D Template by Bill Arcuri, WCSD

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Template by Bill Arcuri, WCSD Who Wants to Be a Millionaire?

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