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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

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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

6943 Views

y=e^(2x) - x^3. Find dy/dx. (please note this is "e to the power of 2x, minus x cubed")

The rules to know are 1) when differentiating e to the power of x... be it 2x or 100x... you bring down the number in front of x, and leave the power as it is. in our case e^(2x) goes to 2e^(2x).

Answered by Toby M. • Maths tutor

7940 Views

Solve the following for X and Y: 2y+4x=14 and x-y=-1

Firstly, Take equation 1 (2y+4x=14) and divide it all by 2. This gives y+2x=7. Next make Y the 'subject' AKA put it on it's own. To do this Subtract 2x from both sides. Now we have Y=7-2X. Here you can se...

Answered by Toby M. • Maths tutor

4986 Views