find the integral of y=x^2 +sin^2(x) with respect to x between the limits 0 and pi

intergal0pi(x^2 + sin^2(x))dx = integral0pi(x^2 + 1/2 - cos(2x)/2)dx since sin^2(x) + cos^2(x) = 1cos^2(x) - sin^2(x) = cos(2x)2sin^2(x) = 1 - cos(2x)thereforeintegral0pi(x^2 +sin^2(x))dx = [(x^3)/3 + x/2 - sin(2x)/4]0pi= ((pi^3)/3 + pi/2 - 0/4) - (0)=(pi^3)/3 + pi/2

Related Maths A Level answers

All answers ▸

Show how '2sin(x)+sec(x+ π/6)=0' can be expressed as √3sin(x)cos(x)+cos^2(x)=0.


How can the y=sin(x) graph be manipulated?


Calculate the binomial expansion of (2x+6)^5 up to x^3 where x is decreasing.


How to find the reciprocal of a graph, such as y=cos(x)?


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