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Maths-

General

Easy

Question

A curve passes through the points given by the following table :

By Simpson’s rule, the area bounded by the curve, the x-axis and the lines x=1, x=4, is

7.583
6.783
7.783
7.275

The correct answer is: 7.783

Area is given by $not stretchy integral subscript x subscript 1 end subscript end subscript superscript x subscript 2 end subscript end superscript y d x equals not stretchy integral subscript 1 end subscript superscript 4 end superscript y d x$
Substituting the given values in the formula
$not stretchy integral subscript 1 end subscript superscript 4 end superscript y d x equals fraction numerator 4 minus 1 over denominator 6 cross times 3 end fraction open curly brackets left parenthesis 2 plus 2.1 right parenthesis plus 4 left parenthesis 2.4 plus 2.8 plus 2.6 right parenthesis plus 2 left parenthesis 2.7 plus 3 right parenthesis close curly brackets$
$equals 7.783$ .

Related Questions to study

With the help of trapezoidal rule for numerical integration and the following table

the value of $not stretchy integral subscript 0 end subscript superscript 1 end superscript f left parenthesis x right parenthesis d x$ is

With the help of trapezoidal rule for numerical integration and the following table

the value of $not stretchy integral subscript 0 end subscript superscript 1 end superscript f left parenthesis x right parenthesis d x$ is

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Then approximate area of cross-section of river by Trapezoidal rule, is

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Then area bounded by x=1 and x=4 by Trapezoidal rule, is

parallel

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By Trapezoidal rule, the area bounded by the curve, the x-axis and the lines x=1, x=5, is

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parallel

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parallel

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In a test of Mathematics, there are two types of questions to be answered–short answered and long answered. The relevant data is given below

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parallel

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parallel

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