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Integrate ⌠( xcos^2(x))dx

We must first use trigonometric identities to simplify cos²(x). We can use the formula cos(A+B) = cos(A)cos(B) - sin(A)sin(B) , where A=x and B=x, so that we ...

Answered by Daniel A. • Maths tutor

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A uniform plank of wood of mass 32 kg and length 4.0 m is used to cross a ditch. In the ditch is a rock, which is used to support the plank horizontally 0.80 m from one end. The other end is supported by the bank. Calculate the rock's supporting force.

We need to calculate moments about a point through which one of the forces is acting. I choose the bank support point. At this point,

moments are caused by the weight of the plank acting at its ce...

Answered by Ricardo S. • Physics tutor

11788 Views

A curve C has equation y = (2 - x)(1 + x) + 3 . A line passes through the point (2, 3) and the point on C with x-coordinate 2 + h . Find the gradient of the line, giving your answer in its simplest form.

First we find the y coordinate which is a function of x:

x = 2+ h so y = (2 - 2 - h)(1 + 2 + h) + 3 = -h² - 3h + 3

Now for the gradient, the line passes through points (2,3) and ...

Answered by Ricardo S. • Maths tutor

3821 Views

To what extent can the English civil war (1642-1651) be described as a war of religion?

The cause's of the English Civil war can be divided into three broad categories, the most important of these being religious division. Politically the fear of Absolutism, caused by Charles stringent refor...

Answered by Ed D. • History tutor

4965 Views

What's the difference between mens rea and actus reus?

Mens rea and actus reus are two elements of a crime, as it would be explained in court. An academic, Wilson, described mens rea as a "mental attitude" - the psychological element of a crime - e....

Answered by Emily B. • Law tutor

3790 Views