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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.
A drug is administrated once every four hours. Let D(n) be the amount of the drug in the blood system at the nth interval. The body eliminates a certain fraction p of the drug duri
round each number to the nearest half 2 over 5
A two-digit number is seven times the sum of its digits. The number formed by reversing the digits is 18 less than the original number. Find the original number.
Additional Rule- Rules of Probability Additional rule is used to calculate the probability of two or more mutually exclusive events. In such circumstances the probability of t
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200 + 406578
4x-5y+16=0
Brian's 100-yard dash time was 2.68 seconds more than one school record. Brian's time was 13.4 seconds. What is the school record? The school record is less than Brian's time.
Objectives After studying this unit, you should be able to briefly describe the developmental stages of children's thinking and learning processes; assess the levels
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