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When integrating by parts, how do I decide which part of the integrand is u or f(x) and which dv or g'(x)?

Integration by parts is not only a very useful techinque for integrating, but it is also one of the techinques that appears more in the IB Mathematics exams. The most important step is to choose the part ...

Answered by Xell B. • Maths tutor

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(Using the Quotient Rule) -> Show that the derivative of (cosx)/(sinx) is (-1)/(sinx).

This question is a typical example aimed to test the student's understanding of the quotient rule, a technique which is used very often in calculus problems. Answer: For a function f(x) = cosx/sinx = u/v,...

Answered by Mark H. • Maths tutor

18245 Views

Why were rallies in Nazi Germany important?

During the Nazis' years in power between 1933 and 1945, Joseph Goebbels was given the very important task of making sure that the Nazi message was effectively spread, through the use of propaganda. One of...

Answered by Francesca W. • History tutor

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Find the integral of xe^(-2x) between the limits of 0 and 1 with respect to x.

We can identify xe^(-2x) as a product and hence we will most probably need to use integration by parts.

We then set u = x and v' = x^(-2x). It is important to do it this way round so that when we d...

Answered by Tom B. • Maths tutor

7653 Views

In which way is a supervolcano different from a volcano and what are the likely consequences of a super volcano eruption?

Super volcanoes are much bigger than normal volcanoes, usually erupting at least 1000 cubic km of material in a single event and far less frequently than normal volcanoes. Normal volcanos erupt nearer to ...

Answered by Jack H. • Geography tutor

7274 Views