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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.
CONSTANTS OF INTEGRATION Under this section we require to address a couple of sections about the constant of integration. During most calculus class we play pretty quick and lo
X and Y are centers of circles of radius 9cm and 2cm and XY = 17cm. Z is the centre of a circle of radius 4 cm, which touches the above circles externally. Given that XZY=90 o , w
Rates of Change or instantaneous rate of change ; Now we need to look at is the rate of change problem. It will turn out to be one of the most significant concepts . We will c
A shuttlecock used for playing badminton has the shape of a frustum of a Cone mounted on a hemisphere. The external diameters of the frustum are 5 cm and 2 cm, and the height of t
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The logarithm of a provided number b to the base 'a' is the exponent showing the power to which the base 'a' have to be raised to get the number b. This number is defined as log a
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Multiplication of complex numbers After that, let's take a look at multiplication. Again, along with one small difference, it's possibly easiest to just think of the complex n
Equations of Planes Earlier we saw a couple of equations of planes. Though, none of those equations had three variables in them and were actually extensions of graphs which we
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