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What is integration?

Integration can be viewed in many ways. The most common way to interpret an integral is to take the area under the curve you would like to integrate. For example Draw y=x, limit between 0 and 1, shade in the...
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Answered by Mikhail S. • Maths tutor
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integrate cos^2(2x)sin^3(2x) dx

To integrate this we need to use the chain rule, substituting cos2x = u Integral becomes: u 2 sin 3 2x dxChain rule: dy/dx = du/dx dy/du du/dx = -2sin2x --> dx = -1/2sin2x du Substituting into the equatio...
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Answered by Lucy W. • Maths tutor
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Why does differentiation work like it does.

Differentiation is about the tangent at a point, from GCSE we have a formula to work out the gradient between two points, in other words, the gradient of the tangent. This means that as the two points get in...
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Answered by Lucas F. • Maths tutor
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(a) Express (1+4*sqrt(7))/(5+2*sqrt(7)) in the form a+b*sqrt(7), where a and b are integers. (b) Then solve the equation x*(9*sqrt(5)-2*sqrt(45))=sqrt(80).

(a) We can ‘get rid of’ a square root in the denominator simply by multiplying by 1 (value of the fraction stays unchanged) in a suitable form. We will take advantage of this formula: (a+b) (a-b)=a^2-b^2. So...
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Answered by Kristina B. • Maths tutor
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Find the equation of the tangent to the curve y=3x^2-7x+5 at the point (2, 3) .

The starting point for a question like this is to differentiate the function - in this case the curve y=3x 2 -7x+5 . We calculate that dy/dx=6x-7 . The question tells us that we are interested in the case wh...
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Answered by Matthew S. • Maths tutor
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