Top answers

Integrate 1 / x(2sqrt(x)-1) on [1,9] using x = u^2 (u > 0).

Differentiate x = u 2 to get dx = 2u du. We need to change the limits, too: 1 <= x <= 9 <==> 1 <= u 2 <= 9 <==> 1 <= u <= 3 (since we are given u > 0). Now we can substitute ...
TD
Answered by Tutor69809 D. • Maths tutor
5284 Views

Show that, for all a, b and c, a^log_b (c) = c^log_b (a).

We want to prove: a log b (c) = c log b (a) . Recall that we can always write x = e ln(x) , so x y = (e ln(x) ) y = e y ln(x) . Recall also the change of basis formula for logs: log b (x) = y <=> b y =...
TD
Answered by Tutor69809 D. • Maths tutor
7488 Views

Use the substitution u=3+(x+4)^1/2 to find the integral of 1/(3+(x+4)^1/2) dx between 0 and 5.

We will call the integral I, so I = integral of 1/(3+(x+4) 1/2 ) dx between 0 and 5. First substitute u=3+(x+4) 1/2 into the equation to get I = integral of 1/u dx between 0 and 5 Next we want to change the ...
CB
Answered by Calum B. • Maths tutor
4318 Views

Find the exact solutions, in their simplest form, to the equations : a) 2ln(2x + 1)-4=0 b)7^(x)e^(4x)=e^5

a) 2ln(2x + 1)-4=0 -> ln(2x + 1)-2=0 -> ln(2x + 1)=2 -> (2x + 1)=e 2 -> 2x = e 2 -1 -> x = (e 2 -1)/2 b) 7 x e 4x =e 5 -> 7 x =e 5 \ e 4x ​​​​​​​-> 7 x =e 5-4x ​​​​​​​-> ln(7 x )=5-4x...
EL
Answered by Elizabeth L. • Maths tutor
5145 Views

How do I find the equation of the tangent to y = e^(x^2) at the point x = 4?

This question can be broken up into two main parts, one you're probably familiar with from C1 + C2 and one which is newer. The first part relates to differentiating a compound function (where a function is d...
SH
Answered by Sam H. • Maths tutor
10062 Views