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Integrate ∫sin²xcosxdx

This indefinite integral (has no defined limits) should be evaluated by integration by substitution This is because you cannot integrate sin 2 xWhen doing integration by substitution, the first thing we need...
RK
Answered by Rachel K. Maths tutor
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Integrate sec^2(x)tan(X)dx

This can be done with integration by substitution. If we let u=tanx then du/dx=sec^2(X). If we substitute U into the integrand we get it being u(sec^2(X))dx. rearranging the du/dx equation to make dx the sub...
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Answered by Amin Z. Maths tutor
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Solve x^2=3(x-1)^2

To start with, we want to put this into quadratic form, where we have ax^2+bx+c=0. We notice that there are terms on both sides of the equation. So we can expand the right hand side and then bring all the te...
JU
Answered by Joshua U. Maths tutor
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How do I work out the exact value of a number which is expressed as an indice, for example 81^-1/4

Firstly, recall the indice rules which are applicable to the question, for example in this question we can use the rules:(x^a)^b = x^abx^-1 = 1/xx^1/2 = square root xSecondly, apply these rules to break down...
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Answered by Cameron H. Maths tutor
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Solve the simultaneous equations 4x + 5y = 13 and 3x - 2y = 27.

Using the elimination method to remove the variable x, we need both equations to have the same values of x. To do this we find the lowest common multiple of the x values: the lowest common multiple of 3 and ...
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Answered by Christy H. Maths tutor
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