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When you are faced with an integral which is a product, such as x.cos(x) , you may be able to integrate it by parts. The statement of the integration by parts is that: ∫u(dv/dx)dx = uv-∫v(du/dx)dx So if you ...

Parametric equations are a set of equations which both depend on the same variable, such as t. An example of this would be: x = 2t 2 ​+1 and y = t ​4 ​-2 As the value of t changes the equations will give you...

A key point to remember here is that a^x could mean the base (a) is not “e”-that special number which has a gradient function, dy/dx (the differential), EQUAL to the function itself, y=e^x. When "a&quot...

By recalling that e ln(a) = a, you can rewrite 3 2x as e 2xln(3) . Then, you can differentiate this like any other e function, by using the product rule. d/dx (e 2xln(3) ) = e 2xln(3) x d/dx (2xln(3)) d/dx (...

First, find the x coordinates of where the lines intersect by setting the equations of the lines equal to each other. Then solve the quadratic (or polynomial) equation. Next, integrate both lines individuall...