Find the value ofthe integral from 1 to 7 of the natural log of x, dx using three rectangles of equal width, with each right end-point used to find the height of each rectangle.

Question

Find the value of using three rectangles of equal width, with each right end-point used to find the height of each rectangle.

 0.5(ln3 + ln5 + ln7) 

0.5(ln1 + ln3 + ln 5) 

2(ln3 + ln5 + ln7) 

ln1 + 2ln3 + 2ln5

Answer 1

Rectangle Area = width•height

Area 1 = (2)(ln(3))

Area 2 = (2)(ln(5))

Area 3 = (2)(ln(7))

Total area = (2)(ln(3)) + (2)(ln(5)) + (2)(ln(7)) = 2(ln(3) + ln(5) + ln(7))