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Integral of (cos(x))^2 or (sin(x))^2

When we try to integrate a function of x, we often use reverse chain rule looking for the derivative of our functions with the power on the side of our integral. However, with these two we do not have an ...

Answered by Arif U. • Maths tutor

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Integrating (e^x)sin(x)

First and foremost, this is an integration of two functions multiplied together and so the first thing that should come to your head is integration by parts from C4. However, when we usually do integratio...

Answered by Arif U. • Maths tutor

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A curve has the equation y=7-2x^5, find dy/dx of this curve

When you differentiate with respect to x, dy/dx, you multiply the number in front of the x by the power of the x then you take one away from the power.So for this example, the 2x⁵ differentiate...

Answered by Emily C. • Maths tutor

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Write cosx - 3sinx in the form Rcos(x + a)

Rcos(x + a) = Rcosxcosa - Rsinxsina
By comparing cosx - 3sinx to the new expression, we can see that:
Rsina = 3 and Rcosa = 1
If we square both and add them, we can see R = √(1²

Answered by Odin G. • Maths tutor

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A) Differentiate ln(x) b) integrate ln(x)

A) y=ln(x) E^y = x E^y(dy/dx ) = 1 E^ln(x)(dy/dx) = 1 X(dy/dx) = 1 Dy/dx = 1/xb) y = 1 * ln(x) V = ln(x) U= x dv/dx =1/x Du/dx = 1xln(x) - (integral) x * (1/x)xln(x) - (integ...

Answered by Stanley R. • Maths tutor

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