Find the area bounded by the curve x^3-3x^2+2x and the x-axis between x=0 and x=1.

To find the area under a curve that is bounded by the x-axis you simply need to integrate the equation of the curve between the limits, so for this equation we will integrate y=x3-3x2+2x with 1 as our upper limit and 0 as our lower limit. To integrate an expression you add 1 to the power and divide by the new power, so the integral of x3-3x2+2x is (1/4)x4-x3+x2. We then substitute x=1 and x=0 into the expression and subtract the resulting values from eachother. When x=1, (1/4)x4-3x3+x2=1/4 and when x=0, (1/4)x4-3x3+x2=0. (1/4)-0=1/4 and so that is our final answer to the question.

JT
Answered by Jack T. Maths tutor

13440 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

A circle with centre C has equation: x^2 + y^2 + 20x - 14 y + 49 = 0. Express the circle in the form (x-a)^2 +(y-b)^2=r^2. Show that the circle touches the y-axis and crosses the x-axis in two distinct points.


Integrate ln(x)


Integrate the function f(x) where f(x)= x^2 +sin(x) + sin^2(x)


How do you differentiate (3x+cos(x))(2+4sin(3x))?


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning