Question

The right-hand endpoint of the kth subinterval is denoted x∗k. What is x∗k (in terms of k and n)? x∗k =_________.

Answer 1

In this problem you will calculate ∫302+4 by using the formal definition of the definite integral: ∫()=lim→∞[∑=1(∗)Δ].

(a) The interval [0,3] is divided into equal subintervals of length Δ. What is Δ (in terms of )? Δ =

(b) The right-hand endpoint of the th subinterval is denoted ∗. What is ∗ (in terms of and )? ∗ =

Answer:

a) Δ= $\frac{3}{n}$

b) $x^{*}_{k} = \frac{3k}{n}$

Step-by-step explanation:

a)  If the interval [0,3] , i.e let a = 0 , b =3 and n=n.

So [0,3] divide into n equal subintervals;

Therefore, the length Δ= $\frac{b-a}{n}$

Δ= $\frac{3-0}{n}$

Δ= $\frac{3}{n}$

b) To calculate $x^{*}_{k}$;

$x^{*}_{k}$ = a + k . Δ          (where n= 0, Δ = $\frac{3}{n}$)

= 0 + k . $\frac{3}{n}$

$x^{*}_{k}$  =  $\frac{3}{k}$