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To answer this we will need to use the product rule which is as follows: For y=uv, dy/dx=u'v+uv' where u' is the derivative of u and v' is the derivative...
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...
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...
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...
By multipying across and using some trigonometric identities we can turn this in to a much simpler quatratic which can be solved using the quadratic formula. This step can be simplified by using the subst...
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