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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 sin²xWhen doing integration by substitu...

Answered by Rachel K. • Maths tutor

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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 ...

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 th...

Answered by Joshua U. • Maths tutor

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Solve 29cosh x – 3cosh 2x = 38 for x, giving answers in terms of natural logarithms

Firstly, we need the equation to be in terms of one cosh argument if possible, which can be done by the identity cosh 2x = 2cosh²x - 1. Upon substitution and simplification we get 6cosh²

Answered by Jacob C. • Maths tutor

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Find the gradient of the tangent to the curve y=4x^2 - 7x at x = 2

First, we differentiate our equation using the power rule:dy/dx = 8x - 7This is the gradient of our tangent, to the original equation, at any point x. So, to calculate the gradient at x = 2, we substitute...

Answered by Luke A. • Maths tutor

4145 Views