use a double integral and trigonometric substitution to find the area of a circle with radius r. use the formula int(cos^2u)du = (1/2)u + (1/4)sin2u + C
so ive gotten this far(split the integral into a quarter, then will multiply by 4)...
4*int(0 to r)*int(0 to sqr[r^2-x^2]) 1 dydx
integrating sqr[r^2-x^2] seems to get messy, so i am assuming my substitution comes in here. but im not sure what it would be
would it be something like cos[sqr(r^2-x^2)/r] ?
there are also 3 other questions, which want me to find the volume of a sphere using triple integrals, and hypervolume of a hypersphere using quadruple integrals, and the volume of a hypersphere using n integrals. however, i think before i start those, i need to figure out the first basic one, but i cant.