Questions from General Calculus


Q: Evaluate the integral. f sin x cos (cos x

Evaluate the integral. f sin x cos (cos x) dx

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Q: Evaluate the integral. f dt/t2 + 6t+

Evaluate the integral. f dt/t2 + 6t+ 8

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Q: Find the area of the region bounded by the given curves.

Find the area of the region bounded by the given curves.

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Q: A trough is filled with water and its vertical ends have the

A trough is filled with water and its vertical ends have the shape of the parabolic region in the figure. Find the hydrostatic force on one end of the trough.

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Q: Evaluate the integral. f03π/2 |sin x|

Evaluate the integral. f03π/2 |sin x| dx

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Q: A gate in an irrigation canal is constructed in the form of

A gate in an irrigation canal is constructed in the form of a trapezoid 3 ft wide at the bottom, 5 ft wide at the top, and 2 ft high. It is placed vertically in the canal so that the water just covers...

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Q: Find the centroid of the region shown. /

Find the centroid of the region shown.

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Q: The demand function for a commodity is given by p = 200

The demand function for a commodity is given by p = 200 – 0.1x – 0.01x2 Find the consumer surplus when the sales level is 100.

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Q: Find the average value of the function f (x) =

Find the average value of the function f (x) = x2 √1 + x3 on the interval [0, 2].

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Q: If f is a continuous function, what is the limit as

If f is a continuous function, what is the limit as f→0 of the average value of f on the interval [x, x + h]?

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