Calculus Answers

Use the method of disks/rings to determine the volume of the solid obtained by rotating the region bounded by y=2x^2 and y=x^3 about the x-axis.

Find the centroid for the region bounded by y=3−e^-X, the x−axis, x=2, and the y−axis.

Decompose (x^2+x+1)/((x+3)(x^2-x+1))

Determine the area of the region bounded by x = y²-y-6 and x = 2y +4.

Determine the area of the region bounded by x = y²-y-6 and x = 2y +4.

Determine the area to the left of g(y) = 3-y2 and to the right of x = -1

Find the area of f(x) = 3+2x-x² above the x-axis.

Find the area, take the elements of the area perpendicular to the x-axis. x²-y+1=0; x-y+1=0.

A farmer wants to fence an area of 60,000 m² in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. What should the lengths of the sides of the rectangular field be (in m) in order to minimize the cost of the fence?

smaller value = m

larger value = m

A poster is to have an area of 630 cm² with 2.5 cm margins at the bottom and sides and a 5 cm margin at the top. Find the exact dimensions (in cm) that will give the largest printed area.

width  = cm

height = cm