How do you graph an integral of f(x) = x?

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To graph the integral of f(x) = x, first calculate the integral, which is ∫x dx = (x²/2) + C, where C represents the constant of integration. This results in a family of parabolas, each corresponding to different values of C. The process involves finding the integral and then plotting the resulting function. Each graph will vary based on the chosen constant, illustrating the concept of a family of curves. Understanding this process is essential for accurately graphing integrals.
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How would you graph the integral of f(x) = x? What is the process to graph an integral?


Thanks
 
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Do you mean to graph this "beauty":
\int x \ dx =\frac{x^{2}}{2}+C

It's a family of parabolas...

Daniel.
 
oh ok. thanks a lot
 
The way to "graph an integral" is to first find the integral (which will involve a "constant of integration") and then integrate! Since you will have a different function for every value of C, you will, as dextercioby said, a "family" of graphs.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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