Find the area bounded by the curve y=(sin(x))^2 and the x-axis, between the points x=0 and x=pi/2

First, use the identity cos(2x)=(cos(x))^2-(sin(x))^2 along with the identity (sin(x))^2+(cos(x))^2=1 to obtain the integral of 1/2*(1-cos(2x)) as it is not possible to integrate (sin(x))^2 straight off with a substitution of u=sin(x). Integrating this gives 1/2*(x+2sin(2x)) between x=pi/2 and x=0Evaluating this gives 1/2*(pi/2 +2sin(pi)-0-2sin(0)). Since sin(pi) and sin(0) are both equal to zero, this yields the answer pi/4. Hence the area is pi/4 units^2.

TL
Answered by Thomas L. Maths tutor

4485 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Mechanics 1: How do you calculate the magnitude of impulse exerted on a particle during a collision of two particles, given their masses and velocities.


Integrate(1+x)/((1-x^2)(2x+1)) with respect to x.


Solve the equation 2log (base 3)(x) - log (base 3)(x+4) = 2


Given that y=4x^3-(5/x^2) what is dy/dx in it's simplest form?


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