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What is horzontal integration?
Horizontal integration is where the slices are parallel to the x-axis, instead of to the y-axis. In this case, you would be integrating f(y)dy, instead of f(x)dx.
Vertical horizontal integration?
Determine the primary benefits that might be sought by consumers of the following products (a) Tooth paste
When you find particular integral then why you not add constantof integration?
Where you refer to a particular integral I will assume you mean a definite integral. To illustrate why there is no constant of integration in the result of a definite integral let me take a simple example. Consider the definite integral of 1 from 0 to 1. The antiderivative of this function is x + C, where C is the so-called constant of integration. Now to evaluate the definite integral we calculate the difference between the value of the antiderivative at the upper limit of integration and the value of it at the lower limit of integration: (1 + C) - (0 + C) = 1 The C's cancel out. Furthermore, they will cancel out no matter what the either antiderivatives happen to be or what the limits of integration happen to be.
What are limits and why you use them?
Limits give upper and lower bounds for integration. One simple example is in finding an enclosed area. The upper and lower limits form vertical lines which enclose an area between the function and the x-axis and then integration from the lower limit (smaller x boundary) to the upper limit (larger x boundary).
How you can defferentiate an integral?
If the upper limit is a function of x and the lower limit is a constant, you can differentiate an integral using the Fudamental Theorem of Calculus. For example you can integrate Integral of [1,x^2] sin(t) dt as: sin(x^2) d/dx (x^2) = sin(x^2) (2x) = 2x sin(x^2) The lower limit of integration is 1 ( a constant). The upper limit of integration is a function of x, here x^2. The function being integrated is sin(t)
