Polynomial Integral Evaluation
Polynomial Integral Evaluation
\[\begin{aligned}
P(x) &= a_0+a_1x+a_2x^2+\cdots+a_nx^n \\
I(x) &= C+a_0x+\frac{a_1x^2}{2}+\frac{a_2x^3}{3}+\cdots+\frac{a_nx^{n+1}}{n+1}
\end{aligned}\]
Variables
I = integral value of the polynomial
C = integration constant
x = evaluation variable
a0 = constant coefficient
a1 = linear coefficient
a2 = quadratic coefficient
a3 = cubic coefficient
a4 = quartic coefficient
Description
What is this formula?
This formula calculates the indefinite integral of a polynomial function. Integration determines the accumulated quantity represented by the polynomial.
When to use it
Use this formula when calculating accumulated values, areas under curves, displacement from velocity or solving calculus problems involving polynomials.
Example
For:
P(x)=2+(3*x)+(4*x²)
Its integral is:
I=C+(2*x)+((3*x²)/2)+((4*x^3)/3)
If x=2 and C=0:
I=4+6+(32/3)
I=20.667
Applications
Integral calculus
Area calculations
Physics equations
Engineering analysis
Signal processing
Numerical integration
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