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thereddevils
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Homework Statement
How do i solve this integral ?
[tex]\int \big( \sqrt{x^{3}+1} + \sqrt[3] {x^{2}+2x} \big) \ dx [/tex]
Homework Equations
The Attempt at a Solution
what is the appropriate substitution to make here
Integral problems with roots of polynomials are mathematical problems that involve finding the integral (or area under the curve) of a polynomial function, with the roots of the polynomial as the limits of integration.
To solve integral problems with roots of polynomials, you first need to determine the polynomial function and its roots. Then, use the fundamental theorem of calculus to evaluate the integral by finding the antiderivative of the polynomial function. Finally, substitute the roots as the limits of integration and solve for the area under the curve.
Integral problems with roots of polynomials are important in mathematics because they allow for the calculation of the area under a curve, which has numerous real-world applications in fields such as physics, engineering, and economics. They also provide a deeper understanding of polynomial functions and their properties.
Yes, there are specific techniques for solving integral problems with roots of polynomials, such as substitution, integration by parts, and partial fractions. The choice of technique depends on the complexity of the polynomial function and its roots.
Yes, integral problems with roots of polynomials can have multiple solutions. This is because there can be multiple ways to find the antiderivative of a polynomial function, and different techniques may yield different results. It is important to check the validity of each solution by substituting it back into the original integral.