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integrate x^2 + 3x + 4

For the x² term we add one to the power, and then divide by 3 to get x³/3 For the next term we add one to the power and divide by the new power to get 3x²/2 We do the same...

Answered by Harry B. • Maths tutor

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Given that the curve y = 3x^2 + 6x^1/3 + (2x^3)/3x^1, find an expression for the gradient of the curve.

To find the gradient of a curve, you simply differentiate the equation of the curve. The first thing I like to do in any differentiation question is to simplify each expression where you can i.e. whenever...

Answered by Temilolaoluwa S. • Maths tutor

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Let y(x) be a function with derivative y'(x)=x^2-2 and y(0) =7. What is the value of y at x = 3?

Integrate to get y(x) = (1/3)x^3 -2x+c where c is a constant. Substitute in our data 7 =y(0) = (1/3)(0)^3 -2*(0) +c = c. So y(x) =(1/3)x^3 -2x+7 and therefore y(3) = (1/3)(3)^3 -2*3 +7 = 9-6+7 = 10

Answered by Dawn B. • Maths tutor

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Find the area bounded by the curve x^3-3x^2+2x and the x-axis between x=0 and x=1.

To find the area under a curve that is bounded by the x-axis you simply need to integrate the equation of the curve between the limits, so for this equation we will integrate y=x³-3x²

Answered by Jack T. • Maths tutor

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Differentiate ln(x^3 +2) with respect to x

The differential of ln(x) is x^-1 or 1/x. Because we have x^3 + 2 inside the bracket we have to differentiate this term also and multiply this with the other term. For example, d/dx of x^3 +2 is equal to ...

Answered by George L. • Maths tutor

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