# Finding area

by physics=world
Tags: None
 P: 96 1. Use left and right endpoints and the given number of rectangles to find two approximations of the area of the region between the graph of the function and the x-axis over the given interval. f(x) = 2x + 5; [0, 2]; 4 rectangles 2. Relevant equations i = n(n+1)/2 3. The attempt at a solution i can find the upper/right endpoint but the left endpoint is difficult. n Ʃ [2(2(i -1)/(n)) + 5](2/n) i = 1 n (2/n)Ʃ [2(2(i -1)/(n)) + 5] i = 1 n (2/n)Ʃ [(4(i -1)/(n)) + 5] i = 1 n n (2/n){(4/n)Ʃ (i -1) + Ʃ 5} i = 1 i = 1 and then i sub the equation in for i and solve but i do not get the right answer. btw the correct answer is 13.
Homework
HW Helper
Thanks
P: 8,912
 Quote by physics=world i = n(n+1)/2
What are i and n in the context of this question?
 n Ʃ [2(2(i -1)/(n)) + 5](2/n) i = 1 n (2/n)Ʃ [2(2(i -1)/(n)) + 5] i = 1 n (2/n)Ʃ [(4(i -1)/(n)) + 5] i = 1 n n (2/n){(4/n)Ʃ (i -1) + Ʃ 5} i = 1 i = 1 and then i sub the equation in for i and solve but i do not get the right answer.
It was ok up to that point. Exactly what substitution did you make?
 P: 96 n is going to equal 4. and i sub in n(n+1)/2 for i in the equation
Homework
No, it's $\sum_{i=1}^n i=n(n+1)/2$.