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for each of the terms in x, the power to which x is raised increases by 1, and then each term is divided by the new power. A constant of integration is introduced because we were not asked to integrate be...

Since we're told the line is straight, the equation of the line will be of the form y = mx + c.The gradient of the line, m, is the change in y divided by the change in x ; m = (3-7)/(5-2) = - 4/3.Therefor...

Each vector line can be simplified into three separate equations in terms of the lines parameter and one of 'x,y and z.' This process can be done for both lines, creating six equations in total. By settin...

(x + 5)² - 5² - 6(x + 5)² - 25 - 6(x + 5)² - 31

Take the integral as 1 x ln(x) instead of just ln(x). Use integration by parts giving two terms, the first is now just xln(x) and the second is the integral of 1 dx. This is easy to integrate giving the f...