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Find ∫(8x^3+6x^(1/2)-5)dx Give your answer in the simplest form.

This is a simple C1 question on basic integration.I find it best to think of integration as 'anti-differentiation' and it's far more simple. Take each power, add one to it, before dividing into the coefficie...
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Answered by Kudzai S. • Maths tutor
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Find the equation of the tangent line to the curve y = 2x^2 - 4x + 3 at the point (3,9)

To find the equation of the tangent line to the curve y = 2x 2 - 4x + 3, we have to differentiate. Taking each part of the equation separately, we can calculate dy/dx = 4x - 4. By differentiating the equatio...
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y = 1/x^2, differentiate y (taken from AQA 2018 past paper)

y = 1/x^2 is the same asy = x^-2 , now we can use the standard differentiation formula nx^n-1 to gety = -2x^-3y = -2/x^3
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Given that y= x^(-3/2) + (1/2)x^4 + 2, Find: (a) the integral of y (b) the second differential of y

This is a typical question for a Core 1 paper. (a) integral of y = (-2)x^(-1/2) + 0.1x^5 + 2x +C Method: Increase the power of x by +1, divide the term through by the new power. (b) dy/dx = (-3/2)x^(-5/2) + ...
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Find the area between the positive x axis and the line given by y=-(x^2)+2x

The first piece of understanding needed to answer this question is that integration can be used to find the area under a graph between two points. However, before we can integrate we must find the bounds bet...
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