Probleemoplossing: volume

A fuel tank mounted on the wing of a jet aircraft is formed by rotating a region about the central axis. This region is formed by rotating a mathematical function about the x-axis and extends from zero to two meters.

To find the volume of the tank, the disk method is used, which involves slicing the solid into infinitesimally thin circular disks perpendicular to the x-axis.

Each disk has an area equal to �� times the square of the function's value. The total volume is found by integrating these areas over the interval.

After squaring the function, the integrand simplifies to a constant multiplied by the second power of x and the difference between two and x.

Expanding and integrating this expression produces an antiderivative involving the third and fourth powers of x.

Evaluating the definite integral from zero to two and substituting the limits gives an expression. Further simplifying yields a volume of approximately 1 cubic meter, which is the total volume of the fuel tank.