Need steps to find the correct answer

Question

Given the table below for selected values of f(x), use 6 left rectangles to estimate the value of

.

x13467910
f(x)	4	8	6	10	10	12	16

Numerical Answers Expected!

Answer for Blank 1:

Answer 1

To find the integral is the same as finding the area under the curve of a line.To find the integral using left sum, construct the rectangles that have a height at the left endpoint, calculate their areas, and add them up. Since the x values do not have a consistent difference (some values are 2 apart, some are 1 apart), you won't have a constant value for delta x. This means you will have to find the areas of 6 rectangles with different bases.

The first rectangle has a height of 4 (the f(1)=4) and a width of 2 (3-1=2), so the area is 6. The next rectangle has a height of 8 (f(3)=8) and a width of 1 (4-1=8), so the area is 8. Following this logic, you find the areas to be 6, 8, 12, 10, 20, and 14. Adding those up, the integral is 70.

Hope that helped!

Answer 2