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Maths-

General

Easy

Question

From the following table, using Trapezoidal rule, the area bounded by the curve, the x-axis and the lines x=7.47, x=7.52, is

0.0996
0.0896
0.6977
0.0776

The correct answer is: 0.0996

Since the area bounded by the x-axis is given by $not stretchy integral subscript x subscript 1 end subscript end subscript superscript x subscript 2 end subscript end superscript f left parenthesis x right parenthesis d x$
According to the table, $not stretchy integral subscript 7.47 end subscript superscript 7.52 end superscript f left parenthesis x right parenthesis d x$
$equals fraction numerator h over denominator 2 end fraction left square bracket y subscript 0 end subscript plus 2 left parenthesis y subscript 1 end subscript plus y subscript 2 end subscript plus y subscript 3 end subscript plus y subscript 4 end subscript right parenthesis plus y subscript 5 end subscript right square bracket$
= $fraction numerator 0.01 over denominator 2 end fraction left square bracket 1.93 plus 2 left parenthesis 1.95 plus 1.98 plus 2.01 plus 2.03 right parenthesis plus 2.06 right square bracket$
= $0.01 divided by 2 left square bracket 1.93 plus 15.94 plus 2.06 right square bracket equals 0.0996$ .

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