@edwardyy.aep: Daily Integral: 114 We have every single trig function squared being added to each other. The way to solve the problem is to break them down using the Pythagorean theorem in different forms. We then simplify by getting a common denominator and flipping the fraction to solve. Notice that we have sin^2 and cos^2 on the numerator which is very close to the double angle identity for sin(2x) that we can manipulate using algebra. At first, the denominator isn’t so easy to simplify, but if you replace cos^2 with 1 - sin^2 and then distribute them, you’ll soon realize that all the functions will simplify down nicely thanks to the Pythagorean theorem again! Afterwards, we will use algebra manipulation again to remove the sine function on top by making it into two integrals; the other one which you can solve in one second. Multiply the integral by 4 on top and bottom to remove the fraction and then multiply by sec again to force out an arctan. It is important that you do a substitution to remove the 2x inside of the sine function. You’ll notice that the top bound will become pi; since sine is symmetrical, you can double the area by making it pi/2 which is very important later on for solving this problem as we will foresee an arctan. Now we need to manipulate the Pythagorean theorem to fully solve using two more substitutions to reveal the arctan. #dailyintegral #integral #calculus

Edwardyy

Open In TikTok:

Region: US

Tuesday 20 October 2026 06:32:20 GMT