Questions from General Calculus


Q: Shade the portion of Fig. 23 whose area is given by

Shade the portion of Fig. 23 whose area is given by the integral 0∫2 [ f (x) - g (x)] dx + 2∫4 [h(x) - g (x)] dx. Figure 23:

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Q: Determine the average value of f (x) over the interval

Determine the average value of f (x) over the interval from x = a to x = b, where f (x) = 2; a = 0, b = 1.

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Q: Determine the average value of f (x) over the interval

Determine the average value of f (x) over the interval from x = a to x = b, where f (x) = 1/x; a = 1/3, b = 3.

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Q: Determine the average value of f (x) over the interval

Determine the average value of f (x) over the interval from x = a to x = b, where f (x) = 1/√x; a = 1, b = 9.

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Q: During a certain 12-hour period, the temperature at time

During a certain 12-hour period, the temperature at time t (measured in hours from the start of the period) was T(t) = 47 + 4t – 1/3 t2 degrees. What was the average temperature during that period?

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Q: Assuming that a country’s population is now 3 million and is growing

Assuming that a country’s population is now 3 million and is growing exponentially with growth constant .02, what will be the average population during the next 50 years?

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Q: Determine the following: ∫7/(2e2x) dx

Determine the following: ∫7/(2e2x) dx

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Q: One hundred grams of radioactive radium having a half-life of

One hundred grams of radioactive radium having a half-life of 1690 years is placed in a concrete vault. What will be the average amount of radium in the vault during the next 1000 years?

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Q: One hundred dollars is deposited in the bank at 5% interest

One hundred dollars is deposited in the bank at 5% interest compounded continuously. What will be the average value of the money in the account during the next 20 years?

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Q: Find the consumers’ surplus for each of the following demand curves at

Find the consumers’ surplus for each of the following demand curves at the given sales level, x. p = 3 – x/10; x = 20

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