What is the integration of TANX COSX?

What is the integration of TANX COSX?

4 Answers. Since tanx=sinxcosx, we have ∫tanxcosxdx=∫sinxcos2xdx=[u=−cosxdu=sinxdx]=∫duu2=−1u+C=1cosx+C.

How do you solve TANX COSX?

First multiply both sides by cosx in order to get tanx = cosx. It then helps to write tanx in terms of cosx and sinx (tanx = sinx/cosx) and if we put this into the equation we now have, we get sinx/cosx = cosx. Then multiply both sides by cosx a second time, to get sinx=cos2x.

What is integral of COSX?

According to the theorem, the integral of cos(x) will be equal to the function that has cos(x) as its derivative plus a constant. By the fundamental theorem of calculus and the fact that the derivative of sin(x) is cos(x), we have that the integral of cos(x) is sin(x) + C, where C is a constant.

What is the derivative of TANX?

sec2x
The derivative of tan x is sec2x. When the tangent argument is itself a function of x, then we use the chain rule to find the result.

Is TANX equal to Sinx COSX?

The tangent of x is defined to be its sine divided by its cosine: tan x = sin x cos x .

What is the derivative of SEC 2x?

The next thing we need to do is multiply the result, f'(g(x) = 2sec x, by the derivative of g(x) = sec x. We know the derivative of g(x) = sec x is g'(x) = secx tanx, so we multiply 2sec x by secx tanx to get our answer. We see that the derivative of sec 2 x is 2sec 2 x tan x.

Is Secx a COSX 1?

The secant of x is 1 divided by the cosine of x: sec x = 1 cos x , and the cosecant of x is defined to be 1 divided by the sine of x: csc x = 1 sin x .

What is the integration of Tanx?

The integral of tan(x) can be solved by rewriting the equation as the integral of sin(x)/cos(x) dx, and then using the integration technique called substitution. Using substitution, the value you will obtain as your answer will be. Take t = cosx. dt = – sinx dx. Substitute the values and you will get.

What is the integration of Tan square X?

The integration of tan squared x is `int` tan2x dx. The trigonometric relation 1 + tan2 x = sec2 x Subtract by 1 on both side. So, we get 1 + tan2 x – 1 = sec2 x – 1

How do you calculate integration?

Calculating integrals is easy when you know how to use your calculator. Open the “Y=” menu of the calculator. It is a light purple button on the left-hand side of the calculator, just below the screen. Graph the curve, “y=f(x).”.

How do you calculate a definite integral?

Definite Integral. A Definite Integral has start and end values: in other words there is an interval [a, b]. a and b (called limits, bounds or boundaries) are put at the bottom and top of the “S”, like this: We find the Definite Integral by calculating the Indefinite Integral at a, and at b, then subtracting: