Use two rectangles of equal width to estimate the area between the graph of f(x)=x+sin( πx) and the x-axis on the interval [4,8]. Evaluate the function at the mid-point of each rectangle to find each height.

Question

a) 20
b) 24
c) 26
d) 28

Thanks in advance

Answer 1

the height of each rectangle is just the function value there.
Since the interval has length 4, each rectangle has width 2.
The interval is divided at x=4,6,8
The midpoint of each sub-interval is at x=5,7
So, your approximation is just
2(f(5)+f(7)) = 2((5+sin(5π))+(7+sin(7π))) = 2(5+7) = 24