## Integral Calculus

The oriented and the absolute content of the area between two function curves in a desired interval, i.e. the two integrals, are calculated

Also are determined:

- the twisting moments for rotation around x-, respectively y-axis,
- the bodies of revolution covered, and
- the arc lengths in the interval [a; b] and
- the center of gravity of the area (if A1=A2).

### Example 1:

ƒ_{1}(x) = 4-x^2 ƒ_{2}(x) = (x-1)^2 Interval from von 0 to 3 Oriented content : A_{1}= 0,00000 Absolute content : A_{2}= 9,50675 Twisting moments : Mx = 9 My = -9 Bodies of revolution : Vx = 56,5487 Vy = -56,5487

### Example 2:

Arc length of the chain line compared to the normal parabola y=x^{2}+1.

ƒ_{1}(x) = cosh(x) ƒ_{2}(x) = x^2+1 Limits of integration from -2 to 2 Oriented content : A_{1}= -2,07961 Absolute content : A_{2}= 2,07961 Arc lengths : L_{1}[a;b] = 7,254 L_{2}[a,b] = 9,294

### Please note:

The integrals are determined using numerical methods. In principle, these reach their limits with functions with a very fast change of sign.

### See also:

Supported FunctionsSetting the graphics