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How do you integrate by parts?

To integrate the product of two functions - say f(x) = xsinx, the product of g(x) = x and h(x) = sin(x) - the we use integration by parts. Since integration is the inverse of differentiation, we'll appeal to...
PK
Answered by Patrick K. • Maths tutor
6722 Views

Given that (2x + 11 )/(2x + 1)(x + 3) ≡ A /(2x + 1) + B /(x + 3) , find the values of the constants A and B. Hence show that the integral from 0 to 2 (2x + 11)/ (2x + 1)(x + 3) dx = ln 15.

First starting from the right hand side. A /(2x + 1) + B /(x + 3) = A(x+3)+B(2x+1)/(x+3)(2x+1) Therefore the numerator = (A+2B)x+(3A+B) Equating this numorator with the Left hand side we are presented with t...
GD
Answered by George D. • Maths tutor
7285 Views

Two identical objects have a charge of magnitude q. If r is the distance bethween them, what should their mass be so that the objects are balanced.

Our first step in this physics problem should be to identify all of the forces that act on the objects. There are two forces here,electrical and gravitational. Since both objects have the same charge in magn...
DK
Answered by Dilyana K. • Physics tutor
3841 Views

Use the Intermidiate Value Theorem to prove that there is a positive number c such that c^2 = 2.

This exercise is asking to prove the existance of the square root of 2. So let's consider the function f(x) = x^2. Since f(x) is a polynomial, then it is continuous on the interval (- infinity, + infinity). ...
DK
Answered by Dilyana K. • Maths tutor
9560 Views

How do I form the subjunctive for regular verbs in French?

The subjunctive is a mood used to express statements which are uncertain, for example, expressing emotion, possibility, necessity or desire. To form the subjunctive for regular verbs (and some irregular ones...
KM
Answered by Kirsty M. • French tutor
3922 Views