Top answers

Use integration by parts to evaluate: ∫xsin(x) dx.

Since our function is a product of two "mini-functions" of x, we are able to use integration by parts.The trick for this is to correctly set 'u' and 'dv'. 'u' should be labelled as the function whi...
BA
Answered by Bailey A. • Maths tutor
4214 Views

Factorise 5x^2 + 20x

Factorising is a way of simplifying an equation by putting it into common parts. In the equation above we can see that x is common to both the 5x^2 and the 20x. If we divide by x and put this in-front of the...
DC
Answered by Dominic C. • Maths tutor
6894 Views

Find where the equation y = x^2 + x - 2 crosses the x-axis.

First, notice that any equation crosses the x-axis when y = 0.Second, notice that x 2 + x - 2 = 0 is an example of a quadratic equation. So, we generally do 1 of 3 things (Factorise, Complete the square or u...
AR
Answered by Asad R. • Maths tutor
3361 Views

Use the factor theorem to show that (x+2) is a factor of g(x)= 4x^3 - 12x^2 - 15x + 50

To prove (x+2) is a factor, the value of x that makes x+2 equal 0 must be substituted into the function g(x) also making g(x)=0. In this case, the value of x being -2 makes x+2 equal to 0 and when substitute...
JR
Answered by James R. • Maths tutor
11140 Views

Find the area bounded be the curve with the equation y = x^2, the line x = 1, the line x = -1, and the x-axis.

The answer is 2/3. This can either be obtained by performing a standard integration of y=x^2, using the power rule, between x = 1 and x = -1. Alternatively, integrate y = x^2 between x = 0 and x = 1, then do...
IA
Answered by Isaac A. • Maths tutor
3887 Views