Reference no: EM131076603

Using integration to derive geometric formulas-

Problem 1- Derive the formula for the circumference of a circle of radius r by computing the arc length of the curve √(r² - x²) from x = -r to x = r.

Problem 2- Derive the formula for the area of a circle of radius r by computing the area between the curves √(r² - x²) and -√(r² - x²) between x = -r and x = r.

Problem 3- Derive the formula for the volume of a sphere of radius r by computing the volume of "the object obtained by rotating the curve √(r² - x²) above the x-axis".

Problem 4- Derive the formula for the volume of a cone whose height is h and whose base has area A by "integrating along the height".