Grade 12Integral Calculus

Integrate root 1+ cos^2xQtehsjsjsjsjsjsjsjsjsjsjsjsjsksjsksjskskskjsjs

Question image for Integrate root 1+ cos^2xQtehsjsjsjsjsjsjsjsjsjsjsj

Siddharth Kedia

9 Years agoGrade 12

2 Answers

Ritika Das

9 Years ago

We know that 1+cos²x = 1+(1 – sin²x) = 2(1 – ((1/2)sin²x). During integration root 2 comes out of the integration sign.

So after integrating we get (root2)E(phi,1/root2) if we consider the upper limit as phi and lower limit as zero!

Swagata

9 Years ago

well at first integrate 1+cos^2x,obviously 1 becomes 0.Now while integrating cos^2x first simplify it to cos2x+1(as cos2x=2cos^2x-1).Then integrate that part,and again 1 becomes 0 and cos2x becomes sin2x/2 but the final answer is sin2x/4 as for bringing that extra 2 earlier u need to multiply ½ to balance the extra 2 .Thus the answer is ---> Sin2x/4