The side of a cube is increasing at a rate of 2 kilometers per hour. At a certain instant, the side is 1.5 kilometers. What is the rate of change of the volume of the cube at that instant (in cubic kilometers per hour)?
What is 13.5
100
Find the area between the curve f(x) = -x2 and the x-axis.
What is 500/3
200
Find the derivative of 12ex
What is 12ex
200
Given [from 2 to 8] f(x) dx = -5 and [from 1 to 2] f(x) dx = -1, find [from 1 to 8] f(x) dx
What is -6
200
Integrate: ∫ (6/x5 dx
What is -(3/2)x-4 + C
200
The side of a cube is decreasing at a rate of 9 millimeters per minute. At a certain instant, the side is 19 millimeters. What is the rate of change of the volume of the cube at that instant (in cubic millimeters per minute)?
What is -9747
200
The graphs of f(x) = x - 4 and g(x) = (x - 4)3 intersect when x = 3, x = 4, and x = 5. What is the total area of the region bounded by the graphs of f(x) and g(x)?
What is 0.5
300
Find the derivative of: 6 cos(4x2)
What is -(48x)sin(4x2)
300
Integrate: [from 0 to 2] (4x3 - 3x2 + 2x)
What is 10
300
Integrate: ∫(6x3 - 4)2 dx
What is (36x7/7) - 12x4 + 16x + C
300
The side of the base of a square prism is increasing at a rate of 5 meters per second and the height of the prism is decreasing at a rate of 2 meters per second. At a certain instant, the base's side is 6 meters and the height is 7 meters. What is the rate of change of the volume of the prism at that instant (in cubic meters per second)?
What is 348
300
What is the total area of the regions bound by the graphs of f(x) = (x - 2)3 and g(x) = x - 2
What is 0.5
400
Find the derivative of (3x2)12sin(4x3)
What is 72sin(4x3)+452x2cos(4x3)
400
Integrate: [from 1 to 2] 12x-5. Round to the nearest thousandth.
What is -2.813
400
Integrate: ∫ (-2√(x) + 4) dx
What is -(4/3)x3/2 + 4x + C
400
One base of a trapezoid is decreasing at a rate of 8 kilometers per second and the height of the trapezoid is increasing at a rate of 5 kilometers per second. The other base of the trapezoid is fixed at 4 kilometers. At a certain instant, the decreasing base is 12 kilometers and the height is 2 kilometers. What is the rate of change of the area of the trapezoid at that instant (in square kilometers per second)?
What is 32
400
The base of a solid S is the region bound by the parabola x2 = 8y and the line y=4. Cross-sections perpendicular to the y-axis are squares.
What is 256
500
Find the derivative of: cos(x)/ln(x)
What is (-xsin(x)ln(x)-cos(x))/(x(ln(x))2)
500
Integrate: [from 9 to 1] -15√(x) dx
What is 260
500
Integrate: ∫ 154(-t2 + 6t) dt
What is -((15t7)/7) + 15t6
500
The side of the base of a square pyramid is increasing at a rate of 6 meters per minute and the height of the pyramid is decreasing at a rate of 1 meter per minute. At a certain instant, the base's side is 3 meters and the height is 9 meters. What is the rate of change of the volume of the pyramid at that instant (in cubic meters per minute)?
What is 105
500
A region is enclosed by the x-axis, the line x = 1, the line x = 3, and the curve y = ex. Write an equation for the volume of the solid created when the region is rotated around the x-axis.