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Integrate by parts. First rewrite the integral in the form udv/dx, which is (1)ln(x). Then integrate (1)ln(x) wrt dx by assigning u=ln(x) du/dx=1/x and dv/dx=1 v=x. We can determine the integral of ln...
a=3 b=7 c=-13
Use quad formula: -b+-root[(b^2-4ac)/2a]
Sub in values: -7+-root[7^2-4x3x-13] =1.22 and -3.55
This is an example of completing the square.If we expand (x - p)^2 + q, we will have x^2 -2px + p + q.Now we can use algebra to work out what p and q are from the following equation. x^2 - 7x + 2 = x^2 -2...
The Ancient Greeks perceived a much stronger relationship between Algebra and Geometry than we do today and because of that they often utilised Geometry to help think about, and solve, certain algebraic q...
Let the parabola be y=x2 and let the family of lines be y=2x+c, in order to study the intersection points we need to consider the second order linear system given by having the two equations ab...
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