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Start by drawing a diagram with all of the information from the question on it, as well as the forces acting on the particle. As forces can be divided into their component parts, we can look at the questi...

When integrating an equation we can treat each variable individually. Lets start with 4x^3, when integrating, we raise the power (in this case 3) by +1 and divide the multiple (in this case 4) by the new ...

First we should simplify the expression to be able to integrate it. We should separate the expression to 2 parts. Now we have the following: 2/x^2 + 4xWe can bring the x^2 to the top,now we have the follo...

First we find the gradient by differentiation. Differentiating the expression for the curve gives dy/dx=2x-2. Subbing in x=-1 gives dy/dx=-4 so the gradient of the line is -4.
To find the y intercep...

One approach would be to use integration by parts, as we have two functions of x within the integral. This approach would get you to the answer but would be more difficult and convoluted than necessary. O...