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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.
Initial Condition(s) are a set of conditions, or a condition on the solution which will permit us to find out that solution which we are after. Initial conditions are frequently a
Alan had 6 books. He read 1/3 of books last week. How many books did Alan read last week?
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find the integral dx/1-x
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1) Find the are length of r(t) = ( 1/2t^2, 1/3t^3, 1/3t^3) where t is between 1 and 3 (greater than or equal less than or equal) 2) Sketch the level curves of f(x,y) = x^2-2y^2
The Definition- The definition of the Laplace transforms. We will also calculate a couple Laplace transforms by using the definition. Laplace Transforms- As the earlier secti
What do you need to multiply 30 by to get 1500? This will give you the top edge length of the rectangle. Can you then figure out what must go below the 30 in order to get the area
f Y is a discrete random variable with expected value E[Y ] = µ and if X = a + bY , prove that Var (X) = b2Var (Y ) .
The 5% sales tax on a basket was $0.70. What was the price of the basket? Use a proportion to solve the problem; part/whole = %/100. The whole is the price of the basket (wh
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