First off, there is no such word in English as "intergral."shn said:i have try to intergral cos^2( x)/sinx. When i used sinx=t i got {[(1-t^2)^n-(1/2)]\t}. When i use intergral by parts i got {cos^2n-1(x)[1-cos^2(x)]} to intergral. If you could give me a tip to intergral this i would bn thankful to you!
An integral trig function is a mathematical function that involves both a trigonometric function (such as sine, cosine, tangent) and an integral (or antiderivative) of that function. It represents the area under a curve of the trigonometric function.
To integrate a trigonometric function, you can use the basic integration rules for trigonometric functions or you can use trigonometric identities to simplify the integral. You can also use substitution or integration by parts to solve more complex integrals.
Some common trigonometric identities used in integral trig functions are:
1. sin^2(x) + cos^2(x) = 1
2. tan^2(x) + 1 = sec^2(x)
3. 1 + cot^2(x) = csc^2(x)
4. sin(2x) = 2sin(x)cos(x)
5. cos(2x) = cos^2(x) - sin^2(x)
6. 1 + tan^2(x) = sec^2(x)
7. 1 + cot^2(x) = csc^2(x)
8. sin(x)cos(y) = (1/2)(sin(x+y) + sin(x-y))
Integral trig functions are used in many real life applications, such as calculating the area under a curve in physics or engineering problems, determining the displacement of an object in motion, and analyzing sound waves and vibrations in music and acoustics.
A definite integral of a trigonometric function has specified limits of integration (upper and lower bounds) and represents the exact area under the curve of the function within those limits. An indefinite integral of a trigonometric function does not have specified limits and represents the general antiderivative of the function. It is often used to find the area under the curve for a range of values or to solve more complex integrals.