What is the signed area between the curve y = x^2 - 4 and the x-axis?

The curve y = x^2 - 4 is a parabola that crosses the x axis at x = - 2 and x = 2, so the area that we are looking for is the area within the parabola when y <= 0 and -2<= x <= 2. So we expect our area to be negative, as this part of the graph of the curve lies under the x-axis.To find the area we integrate the function x^2 - 4 between -2 and 2.The solution to the integral is [x^3/3 -4x] evaluated at 2 minus [x^3/3 -4x] evaluated at -2. That will give the result 16/3 - 16 = -32/3. So the signed area is -32/3 and this is negative as expected.

Related Maths A Level answers

All answers ▸

Differentiate f(x) = 2xlnx.


Find the stationary points of the function f(x) = x^3 - 27x and determine whether they are maxima or minima


What does it mean to differentiate a function?


The expansion of (1+x)^4 is 1 + 4x +nx^2 + 4x^3 + x^4. Find the value of n. Hence Find the integral of (1+√y)^4 between the values 1 and 0 (one top, zero bottom).


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 2013–2024

Terms & Conditions|Privacy Policy