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footmath
- 26
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please solve this integral : \[Integral]Sqrt[1/(u - 1) - 1/u] du
cragar said:so then that just equals cos(x)
cragar said:whoops , I edited my first post and I think it works combine that fraction then complete the square on the bottom. then do a trig substitution .
cragar said:right but when you do the trig substitution it should help with that.
HallsofIvy said:This is your problem. So far you have not shown any attempt yourself.
footmath said:yes . this integral at first was : $ A=\int\sqrt{1+\sin^{2}x}\,dx $
Ray Vickson said:This integral cannot be done in terms of elementary functions. It can, however, be expressed in terms of a so-called "incomplete elliptic integral of the second kind". Are you sure you did not make an error in writing down the problem?
RGV
An integral is a mathematical concept that represents the area under a curve on a graph. It is used to find the total value of a continuously changing quantity, such as distance or volume, by breaking it down into infinitely small pieces.
To solve an integral, you must use a process called integration. This involves finding an antiderivative, which is the opposite of a derivative, and then evaluating the integral at specific upper and lower bounds.
A square root is a mathematical operation that gives the number which, when multiplied by itself, gives the original number. In other words, it is the inverse of squaring a number.
Solving integrals is important because it allows us to find the exact value of a quantity that is changing continuously. This is useful in many fields, including physics, engineering, and economics, where understanding the total value of a changing quantity is crucial.
This integral can be solved using the substitution method. Letting $t = 1-u$, we can rewrite the integral as $\sqrt{\frac{1}{t} - \frac{1}{t+1}}$. Then, by finding the antiderivative and evaluating it at the bounds, we can solve for the final answer.