Integrate x^2e^x with respect to x between the limits of x=5 and x=0.

This question is to test integration by parts.  First let u=x2 and u'=2x as a result, and v'=ex and so v=ex too. Then use the by parts formula to express the integral as x2ex​​​​​​​-2(integral of):(xex​​​​​​​-ex​​​​​​​)dx. Using the by parts method again with the integral we just found we can reduce the second expression to x2ex​​​​​​​-2xex​​​​​​​+2ex​​​​​​​. This is the indefinite integration result of the expression in question, (without the +c!) and the question is finished by first plugging 5 into the answer, to get 25e5-10e5​+2e5​ and then plugging in 0, to give just 2. Subtracting the lower limit from the upper limit results gives 25e5​-10e5​+2e5​-2, which is a constant term and is the answer to the question (in physical terms it is the area underneath the curve y=x2ex between the points x=0 and x=5)

Answered by Alex A. Maths tutor

5312 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

A curve has the equation y = 4x^3 . Differentiate with respect to y.


How do you intergrate basic algebra?


Integrate x*ln(x)


If we have a vector 4x + 6y + z and another vector 3x +11y + 2z then what is the angle between the two?Give the answer in radians


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences