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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.
find the value of x for which [1 0] [0 x-8]
If roots of (x-p)(x-q) = c are a and b what will be the roots of (x-a)(x-b) = -c please explain. Solution) (x-p)(x-q)=c x2-(p+q)x-c=0 hence, a+b=p+q and a.b=pq-c
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Katie's school has a rectangular courtyard whose area can be expressed as 3x 2 - 7x + 2. Which of the following could be the dimensions of the courtyard in terms of x? Since t
Q. What is Common Triangles? Ans. Some triangles appear more commonly than others. You will come across two triangles repeatedly as you learn more about trigonometry. T
Place ten pebbles (or any other such objects) in front of a child who can recite number names upto ten in the correct sequence. Ask him/her to count them aloud while touching the p
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