Questions from General Calculus


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: Evaluate the integral. /

Evaluate the integral.

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Q: Identify the curve by finding a Cartesian equation for the curve.

Identify the curve by finding a Cartesian equation for the curve.

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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: Find the centroid of the region shown. /

Find the centroid of the region shown.

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Q: Find the centroid of the region shown. /

Find the centroid of the region shown.

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Q: Determine whether the series is convergent or divergent by expressing sn as

Determine whether the series is convergent or divergent by expressing sn as a telescoping sum. If it is convergent, find its sum.

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Q: Use integration by parts to prove the reduction formula. /

Use integration by parts to prove the reduction formula.

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

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

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Q: Test the series for convergence or divergence. /

Test the series for convergence or divergence.

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