Answers>Maths>IB>Article

What is the area enclosed by the functions x^2 and sqrt(x)?

First, let's see how the plot of the functions looks like (draw on whiteboard). Next, let's calculate where the functions intersect by setting x2 = sqrt(x) and solving for x (manipulate by squaring both sides and get x4=x and combine to form x(x3-1)=0 which gives x=0 or 1). Finally, find the area by integrating the difference of the functions between these two points (integral from 0 to 1 of sqrt(x)-x2 dx = [2/3 x3/2 -1/3 x3] evaluated from 0 to 1 = 2/3-1/3 = 1/3). Therefore, the area enclosed by the functions x^2 and sqrt(x) is 1/3.

Answered by Maths tutor

1039 Views

See similar Maths IB tutors

Related Maths IB answers

All answers ▸

In a lottery, 6 numbered balls are drawn from a pool of 59. Calculate the probability of scoring a jackpot. There used to be 49 balls in the pool. Calculate by how much the addition of 10 balls has decreased the probability of scoring a jackpot


What is integration by parts, and how is it useful?


Solve the equation sec^2 x + 2tanx = 0 , 0 ≤ x ≤ 2π, question from HL Maths exam May 2017 TZ1 P1


Consider f (x) = logk (6x - 3x 2 ), for 0 < x < 2, where k > 0. The equation f (x) = 2 has exactly one solution. What is the value of k?


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