-dx.jpeg "(2x3-9x2+4x-5) Dx")
Integral of (2x^3 - 9x^2 + 4x - 5) dx
Introduction
In this article, we will explore the integral of the function (2x^3 - 9x^2 + 4x - 5) with respect to x, denoted as dx. This type of integral is known as a polynomial integral.
The Function
The function we are interested in integrating is:
f(x) = 2x^3 - 9x^2 + 4x - 5
This is a cubic polynomial function, which means the highest power of x is 3.
The Integral
To find the integral of f(x) with respect to x, we can use the power rule of integration, which states that:
∫x^n dx = (x^(n+1))/(n+1) + C
where n is the power of x, and C is the constant of integration.
Applying the power rule to each term in the function, we get:
∫(2x^3) dx = (2/4)x^4 + C = (1/2)x^4 + C
∫(-9x^2) dx = (-9/3)x^3 + C = -3x^3 + C
∫(4x) dx = (4/2)x^2 + C = 2x^2 + C
∫(-5) dx = -5x + C
Now, we can combine these terms to find the integral of the entire function:
∫(2x^3 - 9x^2 + 4x - 5) dx = (1/2)x^4 - 3x^3 + 2x^2 - 5x + C
Conclusion
In this article, we have found the integral of the function (2x^3 - 9x^2 + 4x - 5) with respect to x. The result is a polynomial function of degree 4, with a constant of integration C.
