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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.
64% of the students within the school play are boys. If there are 75 students in the play, how many are boys? To ?nd out 64% of 75, multiply 75 by the decimal equivalent of 64%
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as a/b where a and b are coprime positive integers. Find a+b.
A rectangular container is 15 cm wide and 5 cm long, and contains water to a depth of 8 cm. An object is placed in the water and the water rises 2.3 cm. Determine the volume of the
The Daily News reported that 54% of people surveyed said in which they would vote for Larry Salva for mayor. Based on the survey results, if 23,500 people vote in the election, how
in a veggie mix the ratio of cups of carrots to cups of broccolie is 4 to 5 if you made this party mix larger how many cups of carrots would be needed to mix with fo cups of brocco
Unit circle A circle centered at the origin with radius 1 (i.e. this circle) is called as unit circle. The unit circle is very useful in Trigonometry. (b) x 2 + ( y - 3) 2
What is Deductive Reasoning ? Geometry is based on a deductive structure -- a system of thought in which conclusions are justified by means of previously assumed or proved sta
what is a liter
If A, B and P are the points (-4, 3), (0, -2) and (α,β) respectively and P is equidistant from A and B, show that 8α - 10β + 21= 0. Ans : AP = PB ⇒ AP 2 = PB 2 (∝ + 4) 2
A die is rolled twice and the sum of the numbers appearing on them is observed to be 7.What is the conditional probability that the number 2 has appeared at least once? A) 1/3
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