Derive the formula for the circumference of a circle

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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".

Reference no: EM131076603

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