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As there are 2 x terms in the integral we will use integration by parts. Remember;  ∫u*(dv/dx)dx =  uv -  ∫v*(du/dx)dx (found by integrating the product rule). From xcos(x) we need to decide which x term ...

The important part of this question is to really understand what the cosine function looks like, many students will use their calculators to find arccos(0.6) = 53.13 degrees, but not find the other soluti...

Although strictly speaking you get no extra marks for writing out your mathematics clearly and logically, getting into the habit of doing so can help your work in a lot of ways: 1. You ca...

This question is to test integration by parts.  First let u=x² and u'=2x as a result, and v'=e^x and so v=e^x too. Then use the by parts formula to express the integral as x...

df/dx = 4x - 2

turning point when differential = 0 

==>

4x = 2 hence;  x = 0.5

When x = 0.5 f(x) is equal to (substitute) 3.5

hence the turning point is at (0.5,3.5)<...