Consider the region in the first quadrant bounded above by the line and below by the curve

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

Problem

Consider the region in the first quadrant bounded above by the line

y = 4

and below by the curve

y = x^{2}

. Cross sections taken perpendicular to the

x

-axis are equilateral triangles whose bases lie in the region. Determine, in terms of

x

, the length of a side of one such triangular cross section.