# Symmetrical Areas - Page 3

Questions

- Double integrals: #int_0^1 int_(y-1)^(y-3) (x^2+2y) dxdy# ?
- Can you help me with this double integral?
- What is the smallest parameter possible for a rectangle whose area is 16 square inches and what are it’s dimensions?
- Find the area enclosed by the function y=f(x) and x-axis for #f(x)=-x(x-2)(x-4)#?
- An open-top rectangular box is constructed from a 10-in.- by-16-in. piece of cardboard by cutting squares of equal side length from the corners and folding up the sides. Find analytically the dimensions of the box of largest volume and the maximum volume?
- #int int_R e^(-(xy)/2)dA# where #R#:the region bounded by #y=1/4x,y=2x,y=1/x,y=4/x# Evaluate integrals?
- Show that If m and n are Integres? , and m^2 not equal n^2 , then ; integrate cos mx cos nx dx = 0. intervals of integrate {0,2π}
- Explain: What Double Integral represents and write its two applications?
- A soda can is to hold 12 fluid ounces. Find the dimensions that will minimize the amount of material used in its construction, assuming the thickness of the material is uniform?
- Verify whether y^2 is an IF of dx/y+2x/y^2.dy=0?
- A closed rectangular storage bin is to be made so that it has a square base. The volume of the bin must be 8m^3. The material to make the sides costs twice as much as that for the top and the bottom. Find the dimensions of the box that will (- cont.)?
- How to solve this very difficult volume problem involving integration?
- Show that ∫dx from 0 to 1 ∫(x^2-y^2)/(x^2+y^2)dy from 0 to 1=∫dy from 0 to 1 ∫(x^2-y^2)/(x^2+y^2)dx from 0 to 1?
- Evaluate double integral #int int (1-x^2/a^2-y^2/b^2)dx dy # over the first quadrant of the ellipse #x^2/a^2+y^2/b^2 = 1#, by using the transformation #x=au# and #y=bv#?
- How do you solve the following questions?
- An open box is to be made from a rectangular sheet of cardboard od dimension 16cm by 24cm by cutting out squares of = size from each of the four corners & bending up flaps.Find the dimensions of box of largest volume that can be made?
- A rectangular box with a square base and no top is to have a volume of 108 cubic cm. Find the dimensions for the box that will require the least number of material?
- How to evaluate the integral # int s*2^s ds# ?
- What is #int_0^2##int_0^1##ysqrt(y^2 + 7x)#?
- A salt container is to be made in the shape of a cylinder and to contain #500cm^3# of salt. Find the dimensions for the container that requires the least amount of material. Assume the container has a top?