Calculus

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

Thanks in advance

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  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

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