MYTUTOR SUBJECT ANSWERS

579 views

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).

Max S. A Level Maths tutor

2 years ago

Answered by Max, an A Level Maths tutor with MyTutor


Still stuck? Get one-to-one help from a personally interviewed subject specialist

253 SUBJECT SPECIALISTS

Aisling R. A Level Maths tutor, A Level Chemistry tutor
£20 /hr

Aisling R.

Degree: Chemistry (Bachelors) - Bristol University

Subjects offered:Maths, Chemistry

Maths
Chemistry

“Top tutor from the renowned Russell university group, ready to help you improve your grades.”

£22 /hr

Benedict C.

Degree: Natural Sciences (Bachelors) - Leeds University

Subjects offered:Maths, Physics

Maths
Physics

“I am studying Physical Natural Sciences at Leeds University. My sessions focus on understanding and making examples work for you.”

£20 /hr

Ciarán R.

Degree: MEng Civil Engineering with Project Management (Masters) - Leeds University

Subjects offered:Maths, Science+ 1 more

Maths
Science
Geography

“Patient and adaptable Civil Engineering student at the University of Leeds. Contact me to discuss how I can best help you succeed.”

MyTutor guarantee

About the author

£20 /hr

Max S.

Degree: Mathematics (Masters) - Birmingham University

Subjects offered:Maths

Maths

“Top tutor from the renowned Russell university group, ready to help you improve your grades.”

MyTutor guarantee

You may also like...

Other A Level Maths questions

A rollercoaster stops at a point with GPE of 10kJ and then travels down a frictionless slope reaching a speed of 10 m/s at ground level. After this, what length of horizontal track (friction coefficient = 0.5) is needed to bring the rollercoaster to rest?

Integrate ln(x) by parts then differentiate to prove the result is correct

What qualifications and experience do you have at this level?

Differentiate: y=12x(2x+1)+1/x

View A Level Maths tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok