evaluate int_{0}^{1}(x^3+1) as limit of a sum

Question

evaluate      int_{0}^{1}(x^3+1) as  limit of a sum

praxer · Answer

Please help me with this sum.

praxer · Answer

$$ evaluate \int\limits_{0}^{1}  ( X^3+1) as limit of a \sum$$

abb0t · Answer

What?

praxer · Answer

evaluate this as the limit of a sum

abb0t · Answer

Is this linear algebra or calculus II?

praxer · Answer

calculus II

abb0t · Answer

$$\int\limits_{0}^{1}(x^3+1)dx$$

praxer · Answer

yes,

abb0t · Answer

Only cuz i'm really tired right now am I going to give you the answer: $\sf \color{red}{\frac{x^4}{4} +x}$ now evaluate it from 0 < x < 1

praxer · Answer

ohk,

abb0t · Answer

You should know from the Fundamental Theorem of Calculus Pt. II: $$\int\limits_{a}^{b} f(x)dx= F(b)-F(a)$$

praxer · Answer

I know the theorem,

abb0t · Answer

It's area under a curve @Mimi_x3

abb0t · Answer

By definition, if f(x) is continuous on [a,b], then u divide the inteval into n subintervals of equal width, $\Delta$x, and from each interval choise a point, x$_i$, and is defined by as: $$\int\limits_{a}^{b}f(x)dx = \lim_{n \rightarrow \infty} \sum_{i=1}^{n}f(x_i)\Delta x$$

abb0t · Answer

its the net area between a function and the x-axis.