Questions from General Calculus

Q: The base of a solid is the region bounded by the parabolas

The base of a solid is the region bounded by the parabolas y = x2 and y = 2 – x2. Find the volume of the solid if the cross-sections perpendicular to the -axis are squares with one side lying along th...

Q: The height of a monument is 20 m. A horizontal cross

The height of a monument is 20 m. A horizontal cross section at a distance meters from the top is an equilateral triangle with side 1/4x meters. Find the volume of the monument.

Q: Evaluate the integral. f21 x3 lnx dx

Evaluate the integral. f21 x3 lnx dx

Q: Evaluate the integral. f02 (x4 – 3/4x2

Evaluate the integral. f02 (x4 – 3/4x2 + 2/3x -1) dx

Q: Find the length of the curve with parametric equations x= 3t2

Find the length of the curve with parametric equations x= 3t2, y = 2t3, 0 < t < 2.

Q: Use Simpson’s Rule with n = 10 to estimate the length of

Use Simpson’s Rule with n = 10 to estimate the length of the arc of the curve

Q: Find the length of the curve y = 1/6 (

Find the length of the curve y = 1/6 (x2 + 4)3/2, 0 < x < 3.

Q: Find the length of the curve y = fx1√√t,

Find the length of the curve y = fx1√√t, - 1, dt, 1 < x < 16.

Q: A force of 30 N is required to maintain a spring stretched

A force of 30 N is required to maintain a spring stretched from its natural length of 12 cm to a length of 15 cm. How much work is done in stretching the spring from 12 cm to 20 cm?

Q: For what values of m do the line y = mx and

For what values of m do the line y = mx and the curve y = x/ (x2 + 1) enclose a region? Find the area of the region.