Use the limit process to find the area of the region between the graph of the function and the x-axis over the given interval.
y=2x-x^3, [0,1]

Question

Use the limit process to find the area of the region between the graph of the function and the x-axis over the given interval.
y=2x-x^3, [0,1]

anonymous · Answer

$$\int\limits_{0}^{1} (2x-x^3) dx = \left[ x^2 - \frac{ x^4 }{ 4 } \right]_{0}^{1} = 1-\frac{ 1 }{ 4 } = \frac{ 3 }{ 4 }$$
What do you mean by the limit process?

yueyue · Answer

@KSameer73  
An example from my textbook:

anonymous · Answer

Okkkay, that's gonna take some time. Just calculate f(x) for some (say. 10) equally spaced values in  the interval [0,1], add them up, and multiply this sum with 1/10.

anonymous · Answer

In principle

yueyue · Answer

Honestly, I have no idea how to do that. I don't understand anything in this section and the examples in the book just make it more complicated.

anonymous · Answer

Oh... There's an awesome calculus book by Thomas & Finney. You should read Riemann Sums in that book, and be enlightened.