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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.
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
7 divided by 66.5
Polynomials in two variables Let's take a look at polynomials in two variables. Polynomials in two variables are algebraic expressions containing terms in the form ax n y m
Question: a. What is the inverse of f (x)? b. Graph the inverse function from part (a). c. Rewrite the inverse function from part (a) in exponential form. d. Evaluate
If a+b+c = 3a , then cotB/2 cotC/2 is equal to
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In parallelogram ABCD, ∠A = 5x + 2 and ∠C = 6x - 4. Find the evaluation of ∠A. a. 32° b. 6° c. 84.7° d. 44° a. Opposite angles of a parallelogram are same in measu
methods of interpolation
There is a list of the forces which will act on the object. Gravity, F g The force because of gravity will always act on the object of course. Such force is F g = mg
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