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Module 7 the antiderivative
1. Just like any other mathematical operation, the process of differentiation can be reversed. For example,
when we perform the differentiation of ๐(๐ฅ) = ๐ฅ3
.
๐(๐) = ๐๐
๐โฒ(๐) = ๐๐๐โ๐
๐โฒ(๐) = ๐๐๐
Now if you begin with the function ๐(๐) = ๐๐๐
, reversing the process should yield the possible functions
below:
๐(๐) = ๐๐
๐(๐) = ๐๐
+ ๐
๐(๐) = ๐๐
โ ๐
The reversing of the operation of differentiation is known as ANTIDIFFERENETIATION or INDEFINITE
INTEGRATION. If the derivative of ๐(๐ฅ) = ๐ฅ3
is ๐โฒ(๐ฅ) = 3๐ฅ2
, then we say that an antiderivative of ๐(๐ฅ) =
3๐ฅ2
is ๐(๐ฅ) = ๐ฅ3
.
๐(๐) = ๐๐
๐โฒ(๐) = ๐๐๐
โซ ๐โฒ(๐) ๐ ๐ = ๐(๐) + ๐ช
FINDING THE ANTIDERIVATIVE OF A FUNCTION
BASIC INTEGRATION FORMULAS
Differentiation Formulas Integration Formulas
๐
๐ ๐
(๐ช) = ๐ โซ ๐ ๐ ๐ = ๐ช
๐
๐ ๐
(๐๐) = ๐ โซ ๐ ๐ ๐ = ๐๐ + ๐ช
๐
๐ ๐
(๐๐ญ(๐)) = ๐๐ญโฒ(๐) โซ ๐ ๐(๐) ๐ ๐ = ๐ โซ ๐( ๐) ๐ ๐
๐
๐ ๐
(๐ญ(๐) + ๐ฎ(๐)) = ๐ญโฒ(๐) + ๐ฎโฒ(๐) โซ[๐(๐) + ๐(๐)]๐ ๐ = โซ ๐(๐) ๐ ๐ + โซ ๐(๐) ๐ ๐
DERIVATIVE
INTEGRAL