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Why does integration by parts work?

Recall the product rule for differentiation: the derivative of uv is equal to u'v+uv'.If we use the fact that integration reverses differentiation (so the integral of f' is f), then we calculate that uv i...

Answered by Thomas B. • Maths tutor

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The point P(-3,9) belongs to a line intercepting the origin. Find the equation of the line.

We are told that the line passes through the origin O (0,0) and the point P (-3,9). First we need to find the gradient of the line m; this is given by m = (change in y)/(change in x), hence m = (9-0)/(-3-...

Answered by Valeria B. • Maths tutor

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Solve algebraically the simultaneous equations: x^2 + y^2 = 25 and y - 3x = 13

Firstly we should look at the question and notice that the two possible methods are substitution or elimination. We should then notice that since one equation is a quadratic and the other linear, then the...

Answered by Aviv S. • Maths tutor

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A curve has equation 2(x^2)+3x+10. What is the gradient of the curve at x=3

Answered by Tom E. • Maths tutor

3167 Views

A curve has equations: x=2sin(t) and y=1-cos(2t). Find dy/dx at the point where t=pi/6

Since this question concerns parametric's, one may move to eliminate t from the equation to calculate dy/dx directly. However, in this case it is much easier to use the chain rule and realise that dy/dx=d...

Answered by Cameron H. • Maths tutor

4824 Views