This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: dx . This is easy enough to get however. Just solve the substitution for x as follows, Using this substitution the integral is now, So, sometimes, when an integral contains the root the substitution, can be used to simplify the integral into a form that we can deal with. Let’s take a look at another example real quick. Example 2 Evaluate the following integral. Solution We’ll do the same thing we did in the previous example. Here’s the substitution and the extra work we’ll need to do to get x in terms of u . With this substitution the integral is, This integral can now be done with partial fractions. Setting numerators equal gives, Picking value of u gives the coefficients. The integral is then, So, we’ve seen a nice method to eliminate roots from the integral and put into a form that we can deal with. Note however, that this won’t always work and sometimes the new integral will be just as difficult to do....
View
Full Document
 Fall '08
 prellis
 Derivative, Integrals, Mathematics in medieval Islam, Indian mathematics

Click to edit the document details