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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 ...

Answered by Stephi S. • Maths tutor

25156 Views

The novel’s title is deeply ironic - There is nothing ‘great’ about Gatsby - how far do you agree with this view?

Plan: Yes there is nothing great about him: He is a “swindler” and a bootlegger. There is nothing great about someone who undertakes illegal activities in order to get m...

Answered by Nick S. • English Literature tutor

6727 Views

Assess the extent to which China is a threat to the USA's status as the only current superpower.

Split answer into 4 main paragraphs - explain how categories for superpower are largely considered to be economic power, military, geographic and cultural and the answer will attempt to weigh up the exten...

Answered by Nick S. • Geography tutor

13760 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

9464 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 ...

Answered by Mahir Y. • Maths tutor

4529 Views