Consider the region in the first quadrant bounded on the left by the y-axis

MATHEMATICS · Subjective · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

Consider the region in the first quadrant bounded on the left by the y-axis, below by the curve

y = \sin x

, and above by the horizontal line

y = \tfrac{1}{2}

. For every value of

y

in this region, the cross section perpendicular to the y-axis is a rectangle whose height is twice the length of its base. Give a definite integral in terms of

y

that represents the volume of the resulting solid without evaluating it.

Related theory

Area Between Curves
Area Applications
Volume Applications
Applications of Integration

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