Top answers

Integrate cos(4x)+16x^3 with respect to x

This is a simple integration, integrating each individual term with respect to x.For the cos(4x), you should use 'integration by substitution' as it is a function of a function.cos(4x) = cos(u) and u = 4x wh...
AC
Answered by Aadil C. • Maths tutor
4186 Views

When calculating a question with a double integral question between two different ranges which range relates to which integration variable.

When doing double integration with two arbitrary variables, for example 'x' and 'y' look at the Integration on the inside and integrate the function between the given range. For example if the integrand is t...
PV
Answered by Piranavan V. • Maths tutor
3617 Views

How do I differentiate (e^(2x)+1)^3?

You might be tempted to start by expanding the brackets, but in this case it's much easier to use the chain rule. This is the rule that, to differentiate f(g(x)), we find f'(g(x))*g'(x). In other words, to d...
AH
Answered by Alfie H. • Maths tutor
4573 Views

It is given that n satisfies the equation 2*log(n) - log(5*n - 24) = log(4). Show that n^2 - 20*n + 96 = 0.

Given 2log a n - log a (5 n -24) = log a (4) , we can rearrange to have all the "2logs" on one side and the "logs" on the other.So, 2log a n = log a (4) + log a (5 n -24) . Using the laws...
CS
Answered by Cara S. • Maths tutor
5984 Views

Prove that f(x) the inverse function of g(x) where f(x)= - 3x–6 and g(x)= - x/3–2

f ( x ) and g ( x ) are inverse functions when the following equations are true: f ( g ( x ))= x g ( f ( x ))= x To find ( f(g )( x) ) or ( g(f ( x )), use the inner function as the input for the outer funct...
SK
Answered by Sheela K. • Maths tutor
3783 Views