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JCECE Engineering JCECE Engineering Solved Paper-2009

  • question_answer
    Use Simpson's\[\frac{1}{3}\]rule to find the value of \[\int_{1}^{5}{f(x)}\,\,dx\]given
    \[x\] \[1\] \[2\] \[3\] \[4\] \[4\]
    \[y\] \[10\] \[50\] \[70\] \[80\] \[100\]

    A) \[140.88\]                           

    B) \[256.66\]

    C) \[160.26\]                           

    D)  None of these

    Correct Answer: B

    Solution :

    Given that
    \[x\] \[1\] \[2\] \[3\] \[4\] \[4\]
    \[y\] \[10\] \[50\] \[70\] \[80\] \[100\]
    \[{{y}_{0}}\] \[{{y}_{1}}\] \[{{y}_{2}}\] \[{{y}_{3}}\] \[{{y}_{4}}\]
    Let          \[I=\int_{1}^{5}{f(x)}\,\,dx\] Here,     \[h=\frac{5-1}{4}=1\] Using Simpson's \[\frac{1}{3}\] rule \[\int_{1}^{5}{f(x)}dx=\frac{h}{3}[({{y}_{0}}+{{y}_{4}})+4({{y}_{1}}+{{y}_{3}})+2({{y}_{2}})]\]                 \[=\frac{1}{3}[(10+100)+4(50+80)+2(70)]\]                 \[=\frac{1}{3}[110+520+140]=\frac{770}{3}\]                 \[=256.66\]


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