Current location - Training Enrollment Network - Mathematics courses - In higher mathematics, to find the surface area by definite integral, just list the formulas! Don't help me find it ~ write about x and both. I just don't understand the integral inside.
In higher mathematics, to find the surface area by definite integral, just list the formulas! Don't help me find it ~ write about x and both. I just don't understand the integral inside.
It is the same as the formula for finding the length of a curve.

Replace the length of the corresponding line segment on the curve with the length in dx on the tangent passing through point (x, y). (Line Difference)

Or replace the length of the curve with the length of the hypotenuse of a right triangle with dx and dy as right angles:

ds=√((dx)? +(dy)? )=( 1+(dy/dx)? )dx=√( 1+y')dx

Differential of surface area (edge) = rotating perimeter × above ds=2πy.ds=2πy√( 1+y')dx (rotating around X axis)

Integer =∫(x 1, x2)2πy√( 1+y')dx