∫2x(x+2)^(1/2) dx evaluated from 0->2

First make a substitution so we can apply the power rule ∫xn dx = (xn+1)/(n+1) + C more simply. Can see u=x+2 means (x+2)1/2 -> u1/2 and so will help us apply this rule. Change dx/du=1 implies dx = du, and x=0 => u=2, x=2 => u =4 so we now integrate from 2 -> 4.
x=u-2 gives ∫2x(x+2)1/2 dx = ∫2(u-2)(u)1/2 dx = 2∫u3/2 du - 4 ∫u1/2 du. We can now apply the power law above with the new integration limits to obtain the answer (32)/(15) ( 2 + (2)^(1/2) ).

LP
Answered by Luke P. Maths tutor

11553 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Using Pythagoras' theorem, show that sin^2(x)+cos^2(x)=1 for all x.


What are the solutions of (x^3)+6 = 2(x^2)+5x given x = 3 is a solution?


Intergrate 15x^2 + 7


How do I solve x^2 > 6 - x


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