Top answers

Integrate x*ln(x) with respect to x

First identify that integration by parts is required. Then seperate the integration so u = ln(x) dv/dx = x then, du/dx = 1/x v = (1/2)x^2 . And using the integration by parts formula with these substitutions...
AS
Answered by Ana S. • Maths tutor
4461 Views

Derive the following with respect to x1: y=(x1*x2)/(x1+x2).

y is a function of x 1 and x 2 . We are asked to derive y with respect to x 1 , meaning that x 2 remains constant. Note that y ' is the derivative of y. Both the numerator and denominator of the fraction con...
TK
Answered by Thaleia K. • Maths tutor
8886 Views

By using the substitution x = tan(u), find the integral of [1 / (x^2+1) dx] between the limits 1 and 0

First we need to change the limits, and by plugging in 1 and 0 to our substitution we find that the limits for u are arctan(1) and arctan(0) (or pi/4 and 0). Then we need to substitute for dx, and by differe...
OW
Answered by Ollie W. • Maths tutor
12674 Views

The mass of a substance is increasing exponentially. Initially its mass is 37.5g, 5 months later its mass is 52g. What is its mass 9 months after the initial value to 2 d.p?

M=37.5e kt 52=37.5e k 5 52/37.5=e 5k ln(52/37.5)=5k (1/5) (ln(52/37.5))=k k≈0.06538 when t=9, M=37.5e 9*0.06538 M=67.54
RR
Answered by Riccardo R. • Maths tutor
4663 Views

What is the integral of x^(3)e^(x) with respect to x?

This question is looking at integration by parts. Therefore, we need to split the integral into two parts. Part A will be x 3 and Part B will be e x . Draw 2 columns putting Part A in the RIGHT and B in the ...
JB
Answered by James B. • Maths tutor
5425 Views