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Integrate the function f(x)=lnx

This question must be attempted by integration by parts since it cannot be integrated outright and we can thus change the integral to 1 times lnx. We can then use the formula for integration by parts of I...

Answered by Srikant S. • Maths tutor

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What is 12x^6 / 7 divided by 4x^2 / 5 ?

When dividing fractions, the first step is to change the division symbol to a multiplication symbol and flip the fraction that we are dividing by which gives us 12x⁶ / 7 multiplied by 5 / 4x

Answered by Juliette R. • Maths tutor

4181 Views

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 ...

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' va...

Answered by Rachael J. • Maths tutor

9022 Views

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 questi...

Answered by Michael N. • Maths tutor

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