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Integration
We have, so far, seen that differential calculus measures the rate of change of functions. Differentiation is the process of finding the derivative (rate of change) of a function F(x) and is denoted by F'(x) Often, we may know the rate of change, F'(x) of a function F(x) which is unknown to us. In such situations we would like to find out the original function F(x) from the derivative, F'(x). Reversing the process of differentiation and finding out the original function from the derivative is called integration. The original function, F(x) is called the integral.
The left hand side of the equation is read as "the indefinite integral of f(x) with respect to x. The symbol is the integral sign, f(x) is the integrand and 'c' is an arbitrary constant. The arbitrary constant 'c' is added because of the following reason:
If d/dx {F(x)} = f(x) then we can also write that d/dx {F(x) + c} = f(x) where 'c' is an arbitrary constant, because the derivative of any constant is zero.
How to find total no. of unordered pairs of disjoint subsets of a finite set? Solution) Suppose A and B are two such disjoint subsets of the set S. Then every element can go into
what number does not belong 43,47,53,59,65,67
The revenue and cost functions for producing and selling quantity x for a certain production facility are given below. R(x) = 16x - x 2 C(x) = 20 + 4x a) Determine the p
us consider the following mass-spring-damper system: md2xdt2+cdxdt+kx=0 with m=5 kg as the mass of the body, k=1.6N/m as the spring constant and two different values of c.
Are the two angles of a rectangles congruent ? why ?
bananas are on sale for 3 pounds for $2. At that price how many pounds can you buy for $22
calculates the value of the following limit. Solution Now, notice that if we plug in θ =0 which we will get division by zero & so the function doesn't present at this
-3x=-57
multiply 9/19 times 95/7
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