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We want to find the integral of a function at an arbitrary location x from the origin. Thus,
where I(x=0) is the value of the integral for all times less than 0. (Essentially, I(x=0) is the unknown constant of integration or the initial condition.) From the class lecture on the trapezoidal rule for numerical integration, it can be seen that this function can be approximated by
Write a Matlab function to perform numerical integration of a set of evenly spaced data points using the trapezoidal rule. Your function should accept two vectors as inputs, x and f.
The first vector (x) contains the independent variable data (the points at which the values of the function are known. The second vector (f) should contain the values of the function at the points provided in the first vector. Your function should return the integral of f with respect to x, as a function of x.
If α & ß are the zeroes of the polynomial 2x 2 - 4x + 5, then find the value of a.α 2 + ß 2 b. 1/ α + 1/ ß c. (α - ß) 2 d. 1/α 2 + 1/ß 2 e. α 3 + ß 3 (Ans:-1, 4/5 ,-6,
How to raise Powers of Monomials ? To raise a monomial to a certain power: Step 1: Place the entire monomial inside parentheses, and place the desired power outside the paren
Determine y′ for xy = 1 . Solution : There are in fact two solution methods for this problem. Solution 1: It is the simple way of doing the problem. Just solve for y to
what is the derivatives of y=u/5+7 and u=5x-35 using the chain rule?
Estimation of population mean If the sample size is small (n In this case Population mean µ = x¯ ± tS x¯ x¯ = Sample mean S x¯ = s/√n S = standard deviation
approximate the following problem as a mixed integer program. maximize z=e-x1+x1+(x2+1)2 subject to x12+x2 =0
Solve the subsequent quadratic equation: Solve the subsequent quadratic equation through taking the square roots of both sides. 3x 2 = 100 - x 2 Solution: Step 1
Graphical Method While drawing the graph on a natural scale, the independent variables are marked along the horizontal line and corresponding dependen
greens function for x''''=0, x(1)=0, x''(0)+x''(1)=0 is G(t,s)= {1-s for t or equal to s
Determine if the following sequences converge or diverge. If the sequence converges find out its limit. a. {3n 2 - 1 / 10n + 5n 2 } ∞ n =2 b. {e 2n / n} ∞ n =1 c
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