[itex]\displaystyle \frac{1}{\sqrt[3]{x^2}\,}=\frac{1}{x^{2/3}}=x^{-2/3}[/itex]draotic said:Homework Statement
1 / (3√x2 )
Homework Equations
The Attempt at a Solution
the overall power of x in denom becomes ( 1/2 * 2 * 1/3 = 1/3)
taking in num , it becomes (-1/3 + 1 = 2/3) so answer should be x2/3 / (2/3)
which is wrong , please help
Indefinite integration is a mathematical process of finding the most general antiderivative of a given function. It involves reversing the process of differentiation and results in a family of functions that differ by a constant.
The main difference between indefinite and definite integration is that indefinite integration results in a family of functions, while definite integration gives a specific numerical value. Indefinite integration also involves adding a constant of integration, while definite integration involves finding the area under a curve.
Indefinite integration has many practical applications, such as in physics, engineering, and economics, where it is used to find displacement, velocity, acceleration, and other important quantities. It is also used in statistics to find probabilities and in finance to calculate compound interest.
The most common techniques used in indefinite integration include the power rule, substitution, integration by parts, and partial fractions. These techniques allow us to solve a wide range of integrals, including trigonometric, exponential, and logarithmic functions.
You can check your indefinite integral by taking the derivative of the result. If the derivative is equal to the original function, then the integration is correct. You can also use graphing software to plot the original function and its antiderivative to visually confirm the result.