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Use integration by parts to find the integral of x sin(3x)

Firstly we remind ourselves of the integration by parts formula. The formula used to integrate u dv/dx with respect to x = uv - the integral of v du/dx with respect to x. So the first thing we have to decide...
MS
Answered by Marnie S. • Maths tutor
17518 Views

F(X)= 4/(x-3) g(x)= (x+2)/x solve fg(a)= 1

4/(x-3)*(x+2)/x= 4x+8/ x 2 -3x sub in a for x4a+8/a 2 -3athen equate to 1: 4a+8/a 2 -3a=1Times the bottom half of the equation up4a+8=a 2 -3aThe move the 4a+8 across to get a 2 -7a-8=0Factorise (a+1) (a-8)
EJ
Answered by Esther J. • Maths tutor
9022 Views

Complete the square and hence sketch the graph of f(x) = x^2 + 2x + 7

Consider (x + 1)^2, where we halved the coefficient of x to obtain 1. This gives us x^2 + 2x + 1, which looks similar to our function, except it differs by a constant value of 6, hence, by adding 6 to (x + 1...
JP
Answered by Jordan P. • Maths tutor
4332 Views

If I am given a line, how do I find a line that is parallel to it? What about perpendicular?

The key fact here is to remember the relationship between the gradients of lines which are parallel and perpendicular. Two lines that are parallel will always have the same gradient. So if we have a line y =...
HW
Answered by Harry W. • Maths tutor
4770 Views

Differentiate y= 2^x

Initially this looks unlike all the other differentiation questions and seems unsolvable. However the expression 2^x can be rewritten in an equivalent form that will allow us to use the differentiation rules...
MG
Answered by Max G. • Maths tutor
8893 Views