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    Re: MTH603 Assignment 2 Solution and Discussion

    Assignment NO. 2 MTH603 (Fall 2020)

    Maximum Marks: 20
    Due Date: February 15, 2021

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    Question 1:
    Obtain the value of 7c97de1e-5cea-40c2-ae66-caae34020772-image.png using Simpson’s 1/3 rule correct to 3 decimal places.
    MARKS 10
    Question 2:

    Using Newton’s divided difference formula, find the quadratic equation for the following data:

    X 1 2 5
    Y 8 14 44

    Hence find y(3). MARKS 10

  • Cyberian's Gold

    @zareen said in MTH603 Assignment 2 Solution and Discussion:

    Question 1:
    Obtain the value of using Simpson’s 1/3 rule correct to 3 decimal places.
    MARKS 10

    Solution Idea.

    We evaluate the given integral by the formula

    S4=Δx3[f(x0)+4f(x1)+2f(x2)+4f(x3)+2(x4)].

    Determine the width of the subinterval:

    Δx=b−an=1−04=14.

    Compute the function values at the endpoints of the subintervals:

    f(x0)=f(0)=e0=1;

    f(x1)=f(14)=e14=4√e≈1.2840;

    f(x2)=f(12)=e12=√e≈1.6487;

    f(x3)=f(34)=e34=4√e3≈2.1170;

    f(x4)=f(1)=e1=e≈2.7183;

    Plugging in the function values into our equation, we get:

    1∫0exdx≈S4=112[1+4×1.2840+2×1.6487+4×2.1170+2.7183]=112×20.6197=1.7183≈1.718

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