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How do I integrate ∫ xcos^2(x) dx ?

First, recall that when integrating, squared trigonometric functions often cause issues. Therefore, use the identity: cos^2(x) = (cos(2x) + 1)/2 to remove this power, giving the integral: ∫ (xcos(2x))/2 + x/...
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Answered by Stephi S. • Maths tutor
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Solve the simultaneous equation: 2x + y = 5, 3x + 4y = 10

So the aim of simultaneous equations like this, are to figure out the value of x and y. The first thing you have to decide is which one to figure out first. You have to make both 'x' values or both 'y' value...
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Answered by Rachael J. • Maths tutor
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Chris claims that, “for any given value of x , the gradient of the curve y=2x^3 +6x^2 - 12x +3 is always greater than the gradient of the curve y=1+60x−6x^2” . Show that Chris is wrong by finding all the values of x for which his claim is not true.

(Question from AQA A level maths specimen papers) When looking at this question, you need to appreciate the steps required in order to reach the final answer before diving straight in. Firstly, the question ...
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Answered by Michael N. • Maths tutor
9788 Views

Solve the simultaneous equations 2x−3y=12 and 3x + 4y = 8

To solve this question we will first have to think of how we can solve something with two variables. The most common method is through elimination where we remove a variable so then we have an expression for...
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Answered by David S. • Maths tutor
7436 Views

Express (5sqrt(3)-6)/(2sqrt(3)+3) in the form m+nsqrt(3) where m and n are integers. [Core 1]

Step 1: multiply (5sqrt(3)-6)/(2sqrt(3)+3) by (2sqrt(3)-3)/(2sqrt(3)-3) (this is a trick called CONJUGATION as you're really just multiplying the fraction by 1. Step 2: Expand and simplify top and botton to ...
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Answered by Mahir Y. • Maths tutor
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