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Class 12 math (India)

Lesson 15: Review: Riemann sums

Riemann sums challenge

The sum of the areas of the rectangles in the figure below approximates the area under the graph of the function

f, left parenthesis, x, right parenthesis, equals, start fraction, 4, divided by, x, squared, plus, 1, end fraction

above the interval open bracket, 0, comma, 4, close bracket.

Which of the following is the sum of the areas of the rectangles?

(Choice A)
sum, start subscript, n, equals, 1, end subscript, start superscript, 4, end superscript, start fraction, 4, divided by, left parenthesis, 0, point, 5, n, right parenthesis, squared, plus, 1, end fraction
(Choice B)
sum, start subscript, n, equals, 1, end subscript, start superscript, 4, end superscript, start fraction, 4, divided by, left parenthesis, n, minus, 0, point, 5, right parenthesis, squared, plus, 1, end fraction
(Choice C)
sum, start subscript, n, equals, 1, end subscript, start superscript, 4, end superscript, start fraction, 4, divided by, left parenthesis, n, plus, 0, point, 5, right parenthesis, squared, plus, 1, end fraction
(Choice D)
sum, start subscript, n, equals, 0, end subscript, start superscript, 4, end superscript, start fraction, 4, divided by, left parenthesis, n, plus, 0, point, 5, right parenthesis, squared, plus, 1, end fraction
(Choice E)
None of the above

Stuck?