MYTUTOR SUBJECT ANSWERS

457 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

258 SUBJECT SPECIALISTS

£22 /hr

Hannah C.

Degree: Chemistry (Masters) - Durham University

Subjects offered: Maths, Physics+ 2 more

Maths
Physics
German
Chemistry

“About me I am a Chemistry student at Durham university. I am a friendly and paitient tutor, and I belive that anyone can do Maths and Science with practice! I hope to make Science and Maths more approachable and understandable (as wel...”

£22 /hr

Will W.

Degree: Mathematics (Bachelors) - Durham University

Subjects offered: Maths, Physics+ 2 more

Maths
Physics
Further Mathematics
.STEP.

“About Me: I am a Maths and Physics student at Durham University, who has always enjoyed understanding complex concepts in these subjects. I also have a passion for sharing this enjoyment. At my previous school, I ran a Maths Club. Thi...”

£20 /hr

Ellie B.

Degree: Mathematics (Masters) - York University

Subjects offered: Maths, Physics+ 1 more

Maths
Physics
Further Mathematics

“Hi, my name is Ellie and I am currently studying Mathematics at the University of York. I chose York because I felt a real connection with the teachers, they made maths fun, interesting and easy. That's what I hope to do with all my s...”

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

Write tan(3x) in terms of tan(x). Hence show that the roots of t^3 - 3t^2 - 3t + 1 = 0 are tan(pi/12), tan(5pi/12) and tan(3pi/4)

How do I find the integral ∫(ln(x))^2dx ?

How do I find the coordinates of maximum and minimum turning points of a cubic equation?

How do I draw and sketch an equation?

View A Level Maths tutors

Cookies:

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

mtw:mercury1:status:ok