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How do you integrate the term x^2?

When integrating terms that include a power, such as x², there is a simple rule to remember. The rule is to add 1 to the power, and then divide the whole term by this number.For example, in the...

Answered by Jack P. • Maths tutor

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How can I prove that an angle in a semi-circle is always 90 degrees?

If we take the diameter of a circle and create an angle on the circumference at point C of the circle from the two points where the diameter meets the circumference (points A and B), the angle created wil...

Answered by David W. • Maths tutor

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Find the partial fraction decomposition of the expression: (4x^2 + x -64)/((x+2)(x-3)(x-4)).

The first step to solving this question is inputting our dummy variables, and laying out the question so we know what we're doing.
So we end up with:(4x² + x - 64)/((x+2)(x-3)(x-4)) =

Answered by Matt V. • Maths tutor

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Solve the simultaneous equations: 2x+5y=25, x=y+2

using our second equation, we can see that x=y+2. Therefore we can sub x into the first equation. This will give us 2*(y+2)+5y=25. We can go ahead and expand the brackets, which gives us 2y+4+5y=25. We ca...

Answered by Louis W. • Maths tutor

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Given f(x): 2x^4 + ax^3 - 6x^2 + 10x - 84, and knowing 3 is a root of f(x), which is the value of a?

For this exercise we need to be aware of the factor theorem.The factor theorem states when f(c) = 0 then x - c is a factor of the polynomial f(x) and c is a root of f(x). Because we are told that one of t...

Answered by Sabela R. • Maths tutor

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