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RAJASTHAN ­ PET Rajasthan PET Solved Paper-2008

  • question_answer
    Using Simpson's\[\frac{1}{3}\]rd rule, the value of\[\int_{1}^{5}{f(x)}dx\]for the following data is
    \[x\] 1 2 3 4 5
    \[y\] 10 50 70 80 100

    A)  140.88           

    B)  256.66

    C)  160.26           

    D)  None of these

    Correct Answer: B

    Solution :

     Given,
    \[x\] 1 2 3 4 5
    \[y\] 10 50 70 80 100
    \[{{y}_{0}}\] \[{{y}_{1}}\] \[{{y}_{2}}\] \[{{y}_{3}}\] \[{{y}_{4}}\]
    Let \[I=\int_{1}^{5}{f(x)}\,dx\] Here,   \[h=\frac{5-1}{4}=1\] According to Simpson's\[\frac{1}{3}\]rd 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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