Basic Integral Formula

Basic Integral Formula
There are two types of basic integrals: indedeminate and certain integrals.
1. Integral Uncertainty
Here is the basic formula of indede sureness integrals that are very easy to understand: $$\int ax^n~dx=\frac {a}{n+1}x^{n+1}+C$$ The result of an inde baepenal integral is a function with an uncertaintal constant $C$.
Example:
$\displaystyle \int -3x^2~dx=...$
Solution:
$\displaystyle \int -3x^2~dx=\frac{-3}{2+1}x^{2+1}+C$
$\displaystyle =-x^3+C$

2. Specific Integrals
Given $\displaystyle \int f(x)~dx=F(x)+C$, Then the form of certain integrals is: $$\int_b^a f(x)~dx=F(a)-F(b)$$ A particular integral will produce a value.
Example: $$\int_1^4(2x+3)~dx=...$$ Solution: $$\int(2x+3)~dx=x^2+3x+C$$ $$\int_1^4(2x+3)~dx=(4^2+3.(4))-(1^2+3.(1))$$ $$\int_1^4(2x+3)~dx=28-5=23$$
Thus this material, see you in other material and hopefully useful.

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