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When you are asked to integrate a function f(x), you are really being asked the question: "what function F(x) exists such that when you take its derivative, you are left with f(x)?"

Let u...

We know that d / dx (x) = 1. Looking at x^2 as a specific example, and using the product rule, we see that d/dx(x^2) = xd/dx(x) + d/dx(x)x = x + x = 2x. Similarly for x^3, d/dx(x^3) = 3 * x^2 * d/dx(x) = ...

Rearrange first equation to show y=-5/3x-1

lines are parallel therefore gradient is the same

m=-5/3

First "Separate the Variables" by rearranging the equation to get the ys on the LHS and the xs on the RHS:

(1/y) dy=x dx

Now Integrate:

Integral(1/y) dy = Integral(x) dx

Before we begin lets quickly do some reviewing. What are fractions and how can we write them? Fractions are often used when we don't want to write down numbers that are really long. A fraction...