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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.
47x+33y=143
Critical point of exponential functions and trig functions, Let's see some examples that don't just involve powers of x. Example: find out all the critical points for the
Evaluate the volume of a ball whose radius is 4 inches? Round to the nearest inch. (π = 3.14) a. 201 in 3 b. 268 in 3 c. 804 in 3 d. 33 in 3 b. The volume of a
how do i multiply demencinals
Here we know x can only be 1 or -1. so if it is 1 ans is 2. if x is -1, for n even ans will be 2 if x is -1 and n is odd ans will ne -2. so we can see evenfor negative x also an
On dividing the polynomial 4x 4 - 5x 3 - 39x 2 - 46x - 2 by the polynomial g(x) the quotient is x 2 - 3x - 5 and the remainder is -5x + 8.Find the polynomial g(x). (Ans:4 x 2 +
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Keith wants to know the surface area of a basketball. Which formula will he use? The surface area of a sphere is four times π times the radius squared.
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degree of a diffrential equation
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