There several situations in real life that can be modeled with trigonometric functions. Perhaps one of the most famous examples is a vibrating string, as the ones we can see in music instruments. Also, the behavior of the electric current is modeled using trigonometric functions, in particular in a circuit with alternate current. Another example is the movement of a pendulum with short oscillations
The area of the resulting figure will be given by: ∫f(x)dx f(x)=13/2x^3 thus ∫f(x)dx=13/2∫x³dx=13/8[x^4] integrating over the inerval 13/8(12^4)-13/8(5^4) =32680+3/8 sq. units =
