The method is based on a geometrical interpretation of definite integrals. This is applied to cases where the equation for bending moment to be written is cumbersome and the loading is relatively simple.
1. A cantilever is subjected to a concentrated load at the free end.It is required to find out the deflection at the free end.
Fpr a cantilever beam, the bending moment diagram may be drawn as shown below
Let us workout this problem from the zero slope condition and apply the first area - moment theorem
The deflection at A (relative to B) may be obtained by applying the second area - moment theorem
NOTE: In this case the point B is at zero slope.