## Finding area

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.
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Recognitions:
Homework Help
 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?
 n is going to equal 4. and i sub in n(n+1)/2 for i in the equation

Recognitions:
Homework Help
No, it's $\sum_{i=1}^n i=n(n+1)/2$.