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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.
Perform the denoted operation. (4/6x 2 )-(1/3x 5 )+(5/2x 3 ) Solution For this problem there are coefficients on each of term in the denominator thus
Substitution Rule ∫ f ( g ( x )) g′ ( x ) dx = ∫ f (u ) du, where, u = g ( x ) we can't do the following integrals through general rule. This looks considerably
How do I solve step by step 7
Measures of Dispersion - The measures of dispersion are extremely useful in statistical work since they indicate whether the rest of the data are scattered away from the mean
different types of ellipse
y"-3y''-4y=2sinx
Using Substitution Solving Polynomial Equations ? Solve : (x 3 + 4) 2 - 15 (x 3 + 4) + 36 = 0. You might be tempted to multiply everything out and factor. However, there
E1) Create a guessing game for children of Class 2, to familiarise them with the concept of a time interval E2) How could you use group dancing to teach concepts of geometry? Th
In class 1, the teacher had written down the digits 0,1, ...., 9 on the board. Then she made all the children recite the corresponding number names. Finally, she made them write th
#triple integral of x^2+y^2+z^2 over 0
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