Question

Please help me out tired want to sleep

Answer 1

Answer:

The approximate area by Riemann Sum of the curve is represented by $A = 0.4\cdot \Sigma\limits_{t = 1}^{n} [2\cdot (2+0.4\cdot t)^{3} - 4]$.

Step-by-step explanation:

The area below the curve is estimated by the concept of Riemann Sum with right endpoint rectangles, which is defined by the following formula:

$A = \left(\frac{\Delta x}{n} \right) \cdot \Sigma \limits_{t = 1}^{n} g\left (x_{o} + \frac{\Delta x}{n}\cdot t \right)$ (1)

Where:

$A$ - Area below the curve, in square units.

$n$ - Number of rectangles, no units.

$x_{o}$ - Lower bound of the interval, in units.

$\Delta x$ - Length of the interval, in units.

$t$ - Summation index.

If we know that $g(x) = 2\cdot x^{3} - 4$, $n = 10$, $x_{o} = 2$ and $\Delta x = 4$, then the area below the curve is represented by the following equation:

$A = 0.4\cdot \Sigma\limits_{t = 1}^{n} [2\cdot (2+0.4\cdot t)^{3} - 4]$