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I often find it difficult to remember all the different identities, so what is useful is instead to just remember the familiar identity sin^2(x) + cos^2(x) = 1 that we have come across many times, and div...
Recall the product rule for differentiation. If y=uv, where u and v are functions defined by functions of x, then we can take the derivative of y as: y'=u'v+v'u () (where ' denotes the derivative) ...
First, we use the trig identities: cos2x=cos^2x-sin^2x, cos^2x+sin^2x=1 and sin2x=2sinxcosx to transform the integral to ∫(cos2x)/(1+sin2x)dx.We know that ∫f'(x)/f(x)dx = ln|f(x)|+c, so we let f(x)=...
First, multiply throughout by the denominator of the main function to give as follows: 4-2x = A(x+1)(x+3) + B(2x+1)(x+3) + C(2x+1)(x+1) Then, choose values of x which will cause two of the constants to va...
I would go through a similar example of integration with the student using the whiteboard and would explain the use of integration, and would then get them to do the above question, giving them hints when...
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