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Prove that the indefinite integral of I = int(exp(x).cos(x))dx is (1/2)exp(x).sin(x) + (1/2)exp(x).cos(x) + C

Starting with the initial integral of int(exp(x).cos(x))dx we can see that this is going to have to be integrated by parts. This states that the integral of (u . dv/dx)dx is equal to u.v - int(v . du/dx)dx T...
SA
Answered by Sammy A. • Maths tutor
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A curve has the equation y = x^4 - 8x^2 + 60x + 7. What is the gradient of the curve when x = 6?

To find the gradient of any curve, we take the derivative. So in this case, we need to take dy/dx. We do this by multiplying the term by the power on x, and then lowering the power by one. For example, for t...
EH
Answered by Elizabeth H. • Maths tutor
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What are the key points of Sutherland's (1939) Theory of Differential Association?

Key points include: Criminal behaviour... 1) is learnt. Southerland is behaviourist in this respect. 2) is learnt through social interaction and communication. Bandura (1961) disagrees, as mere observation i...
WL
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How to learn vocab?

Learning vocab is not easy and different methods work for different people. Here are just a few suggestions of ways to try... Mind maps I find it very effective to categorise vocab e.g. Technology. Then for ...
ES
Answered by Ellie S. • Spanish tutor
3191 Views

Integrate xsin(x) by parts between the limits of -pi/2 and +pi/2

Let u = x and dv/dx = sin(x), By using the general expression of: integral(u multiply dv/dx)dx = [u multiply v] - integral(v multiply du/dx)dx, and by realising that: du/dx = 1, and v = -cos(x), we can deduc...
MB
Answered by Matthew B. • Maths tutor
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