thanks a million your graph with the explantion of Charle link is just awsome!BvU said:
A triple integral in cylindrical coordinates is a mathematical concept used to calculate the volume of a three-dimensional shape with cylindrical symmetry. It involves integrating a function over a region in three-dimensional space, taking into account the cylindrical coordinates of the points in that region.
A triple integral in cylindrical coordinates differs from a regular triple integral in that it takes into account the cylindrical coordinates of the points in the region being integrated over. This means that instead of integrating over a rectangular region in three-dimensional space, the region is described in terms of cylindrical coordinates (radius, angle, and height).
Cylindrical coordinates are advantageous for a triple integral because they simplify the integration process for shapes with cylindrical symmetry. This is because the cylindrical coordinates are aligned with the axes of the shape, making the integration boundaries easier to define and the integral easier to evaluate.
Some common problems encountered when using cylindrical coordinates for a triple integral include defining the correct integration boundaries, converting the function being integrated into cylindrical coordinates, and visualizing the shape in three-dimensional space. It is also important to pay attention to the order of integration when setting up the integral.
To solve a problem with a triple integral in cylindrical coordinates, you should first carefully define the region of integration and convert the function into cylindrical coordinates. Then, you can evaluate the integral using the appropriate integration techniques, such as using the substitution method or using symmetry to simplify the integral. It is also helpful to visualize the shape and refer to mathematical tables for common integrals in cylindrical coordinates.