MTH603 Assignment 2 Solution and Discussion

Re: MTH603 Assignment 2 Solution and Discussion
Assignment NO. 2 MTH603 (Fall 2020)
Maximum Marks: 20
Due Date: February 15, 2021DON’T MISS THESE: Important instructions before attempting the solution of this assignment:
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Also remember that you are supposed to submit your assignment in Word format any other like scan images etc. will not be accepted and we will give zero mark corresponding to these assignments.Question 1:
Obtain the value of 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 44Hence find y(3). MARKS 10

@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 10Solution 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