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= [tex]\frac{3}{n}[/tex]
b) [tex]x^{*}_{k} = \frac{3k}{n}[/tex]
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= [tex]\frac{b-a}{n}[/tex]
Δ= [tex]\frac{3-0}{n}[/tex]
Δ= [tex]\frac{3}{n}[/tex]
b) To calculate [tex]x^{*}_{k}[/tex];
[tex]x^{*}_{k}[/tex] = a + k . Δ (where n= 0, Δ = [tex]\frac{3}{n}[/tex])
= 0 + k . [tex]\frac{3}{n}[/tex]
[tex]x^{*}_{k}[/tex] = [tex]\frac{3}{k}[/tex]
