- #1
y33t
- 107
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As the title obviously states, how can I evaluate this integral by hand ? I know the result of it, I need to learn how to do it.
∫(z2+x2)-3/2dx
Thanks in advance.
∫(z2+x2)-3/2dx
Thanks in advance.
arildno said:Letting "x" be the variable to integrate first, set x=z*Sinh(u), where Sinh(u) is the hyperbolic sine function.
No.y33t said:I didn't get it, it's from a simple example from a textbook. There should be a simpler way of doing this because it just skips the evaluation of this integral and directly passes to the result as if it's "that" easy to do. Any simpler solutions ?
dextercioby said:x=z tan t can also do the trick.
There are several methods for computing integrals, such as substitution, integration by parts, and partial fractions. The best method to use will depend on the specific integral and your comfort level with each method. It is important to review the integral and try multiple methods to determine which one is most suitable.
Yes, there are many online calculators and computer programs that can help you compute integrals. However, it is important to understand the steps and methods used to compute the integral, as relying solely on a calculator or program may not always be accurate or helpful.
Improper integrals are integrals that have one or both limits of integration at infinity or have a discontinuity within the interval. To compute these integrals, you can use a limit of integration that approaches infinity or use a change of variable to make the integral finite. It is important to carefully analyze the integral and determine the best approach for handling it.
While there are certain techniques and methods that can make computing integrals easier, there is no shortcut or trick that can be applied to all integrals. It is important to have a solid understanding of the fundamental principles of integration and to practice solving various types of integrals.
Integrals are used to determine the area under a curve and to solve various mathematical problems in physics, engineering, economics, and other fields. They are also used in the process of finding antiderivatives and solving differential equations. Overall, computing integrals helps us understand the relationship between a function and its derivative and has practical applications in many areas of science and mathematics.