Given that dx/dt = (1+2x)*4e^(-2t) and x = 1/2 when t = 0, show that ln[2/(1+2x)] = 8[1 - e^(-2t)]

1/(1+2x) dx = 4e^(-2t) dt      Integrate both sides:   ln[2/(1+2x)] = -8e^(-2t) + c      input x = 1/2, t = 0:  ln(2/2) = -8*(1) + c        ln 1 = 0,  so c = 8ln[2/1+2x] = 8[1-e^(-2t)]

HF
Answered by Henry F. Maths tutor

2925 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Expand using binomial expansion (1+6x)^3


Find the stationary points on y = x^3 + 3x^2 + 4 and identify whether these are maximum or minimum points.


Given that log3 (c ) = m and log27 (d )= n , express c /(d^1/2) in the form 3^y, where y is an expression in terms of m and n.


How do you integrate by parts?


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences