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How do I know if I am using the right particular integral when solving a differential equation

Particular integrals will generally be derived in two different ways, depending on the type of the differential equation that you are solving. For example if it was a linear first order ODE, then you woul...

Answered by Vaikkun V. • Maths tutor

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Use the substitution u=4x-1 to find the exact value of 1/4<int<1/2 ((5-2x)(4x-1)^1/3)dx

We are required to solve this integral using integration by substitution, in which we assign a variable to equal a certain region of the integrated function in this case, 4x-1. The purpose of this is to r...

Answered by Taylor R. • Maths tutor

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If given two parametric equations for a curve, how would you work out an equation for the gradient?

Parametric equations will have both the x and the y coordinates expressed in terms of another paramater, usually t. Gradients of curves are expressed in the form of an equation of dy/

Answered by Mollie W. • Maths tutor

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Show that Sec2A - Tan2A = (CosA-SinA)/(CosA+SinA)

Sec2A - Tan2A Definition of Sec and Tan = 1/Cos2A - Sin2A/Cos2A Combining Fractions = (1 - Sin2A) / (Cos2A) Apply Double Angle Formula = (1 - 2SinACosA) / (Cos²A - Sin²A) Make use of...

Answered by James C. • Maths tutor

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