# Finding area

by physics=world
Tags: None
 P: 104 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: 9,857
 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: 104 n is going to equal 4. and i sub in n(n+1)/2 for i in the equation
Homework
No, it's $\sum_{i=1}^n i=n(n+1)/2$.