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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.
A circle touches the side BC of a triangle ABC at P and touches AB and AC when produced at Q and R. Show that AQ= 1/2 (perimeter of triangle ABC) Ans: Since the length o
The angle of elevation of the top of a tower from a point on the same level as the foot of the tower is α. On advancing 'p' meters towards the foot of the tower, the angle of eleva
The volume of grains in a silo at a particular time (measured in hours) is given by V (t) = 4t(3-t) m3. Find the rate of change of the volume of grains in the silo from first princ
The measures of the angles of a triangle are in the ratio of 3:4:5. Evaluate of the largest angle. a. 75° b. 37.5° c. 45° d. 60° a. The addition of the measures of t
Evaluate the convergence of the algorithms: From the convergence proof of power method, LR and QR algorithm for the computation of eigenvalues we see that the easiest case to
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Two circles touch externally. The sum of their areas is 58 π cm 2 and the distance between their centres is 10 cm. Find the radii of the two circles. (Ans:7cm, 3cm) Ans:
Define symmetric, asymmetric and antisymmetric relations. Ans: Symmetric Relation A relation R illustrated on a set A is said to be a symmetric relation if for any x,
Arc Length and Surface Area Revisited We won't be working any instances in this part. This section is here exclusively for the aim of summarizing up all the arc length and su
Difference Between Experiment and Outcome Experiment is an operation that produces outcomes which can be observed. Outcome/Event is the result of an experiment.
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