Integrals of Polynomial functions
Integrals of polynomial functions form a fundamental aspect of calculus, serving as a cornerstone in mathematical analysis and problem-solving. These integrals, arising from the process of finding the area under the curve of polynomial equations, exhibit straightforward computational techniques due to the linearity of integration and the well-defined nature of polynomials. Understanding the integration of polynomial functions not only facilitates the computation of areas and volumes but also lays the groundwork for more advanced calculus concepts and their applications in diverse fields such as physics, engineering, and economics.
Questions
- What is #int 4 x^5 -7 x^4 + 3 x^3 -8 x^2 -4 x + 1 dx#?
- What is the antiderivative of #(x+1)^2#?
- How do you find the indefinite integral of #int (-2x^-3+10x^-5) dx#?
- How do you integrate this? #int_0^1(x^4(1-x)^4)/(1+x^2)dx#
- How do you find the indefinite integral of #int (3x^-2-4x^-3)dx#?
- How do you find the antiderivative of #(5x^2)/(x^2 + 1)#?
- How do you integrate #int x^3*(1-x^4)^6 dx #?
- How to find (f) if f′(x)=16x^3+6x+7 and f(1)=−1 ?
- How do you integrate #x^15 dx#?
- How do you find the antiderivative of #f(x)=-1/2x^3+2x^2-3x-2#?
- How do you find the indefinite integral of #int -24x^5 dx#?
- How do you integrate #int (2t^2-1)^2dt#?
- How do you find the most general antiderivative of the function #f(x) = x(8 - x)^2#?
- What is the antiderivative of #f(x) = x - 7#?
- What is #int (4 x^5 -7 x^4 + 9 x^3 -8 x^2 +2 x + 1) dx#?
- How do you find the indefinite integral of #int (4sinx)/(3tanx)dx#?
- How do you integrate #int (1+3t)t^2dt#?
- How do you integrate #dy / (4(y^(1/2))#?
- How do you integrate #{x(sqrt(1+x^2)} dx# from 0 to 1?
- How do I evaluate #int_1^4sqrt(t) \(5 + 2 t) dt#?