- #1
belleamie
- 24
- 0
for the life of me i can't seem to understand how to the the intergral of dx/ (1+cos ^2(x))?
The formula for calculating the integral of dx/ (1+cos ^2(x)) is ∫ dx/ (1+cos ^2(x)) = tan(x) + C, where C is the constant of integration.
To solve the integral of dx/ (1+cos ^2(x)), you can use the substitution method by substituting u = cos(x) and du = -sin(x) dx. This will transform the integral into ∫ du/ (1+u^2), which can be solved using the arctan formula.
The domain of the integral of dx/ (1+cos ^2(x)) is all real numbers, while the range is also all real numbers.
Yes, the integral of dx/ (1+cos ^2(x)) can be used to find the area under a curve. It represents the antiderivative of the function, and the definite integral can be used to find the area under the curve between two given points.
Yes, apart from the substitution method, the integral of dx/ (1+cos ^2(x)) can also be solved using the trigonometric identity cos^2(x) = (1+cos(2x))/2. This will transform the integral into a simpler form that can be solved using basic integration techniques.