How to integrate e^(5x) between the limits 0 and 1.

Note that by the chain rule if the function y is such that y(x)=f(g(x)), where f and g are functions, then the derivative of y wrt x is given by

dy/dx = (df/dg)*(dg/dx).

Hence if we let the function y be e^(5x) and g(x)=5x then y(x)=e^(g(x)). Then by the chain rule as detailed above dy/dx = 5*e^(5x).

Note that this is similar to the function we're integrating e^(5x). In fact the derivative of (1/5)*e^(5x) is e^(5x). Let F(x) be this function.

Hence the value of the integral between the limits 0 and 1 is the difference of this function evaluated at the limits, that is F(1)-F(0) which is (1/5)*(e^(5)-1).

MS
Answered by Max S. Maths tutor

10955 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Find the value of x in (4^5⋅x+32^2)⋅2^5=2^16⋅x


Let y = x^x. Find dy/dx.


y = Sin(2x)Cos(x). Find dy/dx.


You're on a game show and have a choice of three boxes, in one box is £10, 000 in the other two are nothing. You pick one box, the host then opens one of the other boxes showing it's empty, should you stick or switch?


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