# Consider the integral given by [a,b]=[0,4]. (a) Find an approximation to this integral by using a Riemann sum with right endpoints and n = 8. Your answer should be correct to four decimal places. R8= ?

Aug 28, 2015

I assume that you are trying to find the right Riemann sum for some function $f$ with the given $n$ and the interval $\left[0 , 4\right]$

#### Explanation:

The equality $\left[a , b\right] = \left[0 , 4\right]$ does not give an integral.

I assume that we have some integral given by ${\int}_{a}^{b} f \left(x\right) \mathrm{dx}$, with $\left[a , b\right] = \left[0 , 4\right]$.

With $n = 8$, we get $\Delta x = \frac{4 - 0}{8} = 0.5$

So the right endpoints of the subintervals are:

$0.5 , \text{ " 1," " 1.5," " 2," " 2.5," " 3," " 3.5, " and } 4$

The desired Riemann sum is:

${R}_{8} = \left[f \left(0.5\right) + f \left(1\right) + f \left(1.5\right) + f \left(2\right) + f \left(2.5\right) + f \left(3\right) + f \left(3.5\right) + f \left(4\right)\right] 0.5$

Once you know what the function is, you can do the arithmetic.

Aug 29, 2015

#### Explanation:

This is the question.