Question

onsider the following limit of Riemann sums of a function f on​ [a,b]. Identify f and express the limit as a definite integral. ModifyingBelow lim With Upper Delta right arrow 0Summation from k equals 1 to n (x Subscript k Superscript star )Superscript 4 Baseline Upper Delta x Subscript k​; ​[6​,10​].

Answer 1

Answer:

The solution is given as $\int_{6}^{10} x^4dx$

Step-by-step explanation:

It is given that

$\lim_{\Delta \to 0} \sum_{k=1}^{n}(x_{k}^{*})^4\Delta x_{k} \, \,\,\,\,\,\,\,\,\, [6, 10]$

As

$\int_{a}^{b} F(x)dx=\lim_{\Delta \to 0} \sum_{k=1}^{n}(x_{k}^{*})\Delta x_{k}$

where a and b are the lower and upper limits of the bound respectively.

On comparison it is observed that

• a=6
• b=10

• $F(x)= x^4$

So the equation is given as

$\lim_{\Delta \to 0} \sum_{k=1}^{n}(x_{k}^{*})^4\Delta x_{k}\\=\int_{6}^{10} x^4dx$

So the solution is given as $\int_{6}^{10} x^4dx$