Using the substitution of u=6x+5 find the value of the area under the curve f(x)=(2x-3)(6x+%)^1/2 bounded between x=1 and x=1/2 to 4 decimal places.

dx=du/6 => (u-5)/6=x So the integral is now (2((u-5)/6)-3)(u^1/2) du/6 Which through simplifying becomes (1/36)(2u-28)(u^1/2)du = (1/36)(2u^3/2 -28u^1/2)du After integrating becomes (1/36)(4(u^5/2)/5 -56(u^3/2)/3) Bounded between u=11 and u=8 by the substitution After evaluating we reach our final answer of -2.2889 to 4dp

JT
Answered by Joseph T. Maths tutor

3622 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Let X be a normally distributed random variable with mean 20 and standard deviation 6. Find: a) P(X < 27); and b) the value of x such that P(X < x) = 0.3015.


What is a 'derivative'?


How do I find the nature of a stationary point


If I have the equation of a curve, how do I find its stationary points?


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