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Integrate exp(2x)cos(8x) by parts

Let u=exp(2x) and v'=cos(8x)From these you can obtain u' and vu=2exp(2x) and v=1/8 sin(8x)Formula: integral(uv'dx)=uv-integral(vu'dx)=1/8 exp(2x)sin(8x)-integral(1/4 sin(8x)exp(2x))=1/8exp(2x)sin(8x)+1/16cos...
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Answered by Chloe D. • Maths tutor
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Solve the equation 8x^6 + 7x^3 -1 = 0

The first thing to recognise is this is a quadratic in disguise, therefore we can rewrite the equation in terms of a new variable y. Where y=x 3 The equation then becomes 8y 2 +7y-1=0 . We then factorise thi...
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Answered by Kelan P. • Maths tutor
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Integrate sinxcosx dx

Since the question is a trigonometry question, we shall use integration by recognisation, in which case, we found out that the derivative of sin x is cos x.Therefore by chain rule, we can integrate the funct...
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Answered by Harris L. • Maths tutor
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Sketch the curve y = (2x-1)/(x+1) stating the equations of any asymptotes and coordinates of the intersection with the axis. As an extension, what standard transformations from C1 could you use on y=1/x to get this curve?

A good way to start with any of these questions is to guess what type of curve this is, and if that is too difficult then the next best thing is to find some points. In this case it is obvious that it is a h...
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Answered by Alex D. • Maths tutor
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Differentiate x^3 + 6x + 1

Though you are required to understand differentiating from first principles for the exam, questions such as this become quite straightforward once you know the trick. To differentiate all you have to remembe...
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Answered by Myles J. • Maths tutor
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