What is the integration of log sin 2x?
Answer. Answer = – π Log 2.
What is integration of sin x 2?
The integral of sin2x is denoted by ∫ sin2x dx and its value is (x/2) – (sin 2x)/4 + C.
What is integration of LOGX?
The integration of log x is equal to xlogx – x + C, where C is the integration constant. We can evaluate the integral of ln x (integration of log x with base e) using the integration by parts formula (also known as the UV formula of integration).
What is the integration of x 2?
The integration of x^2 is equal to x3/3 + C, where C is the constant of integration. The integral of x^2 gives the area under the curve of the function f(x) = x2.
What is the integration of Cos 2x?
The integral of cos 2x is ∫ cos 2x dx = (sin 2x)/2 + C.
What is integration of log 2x?
Solution:- ∫log(2x) Now integrating by parts. log(2x).(x)−∫12x.(2)(x)dx.
What is integration of X?
Integration of x refers to the process of finding the antiderivative of x. In other words, integration of x is the same as finding the antiderivative of x. The general form of integration is given as ∫f(x) dx.
What is the value of integrating log(SiNx) from 0 to π/2?
Note that integrating log (sinx) from 0 to π / 2 is the same as integrating log (cosx) so that ∫π / 2 0 log (sinx)dx = 1 2∫π / 2 0 log (sinxcosx)dx = 1 2∫π / 2 0 log (sin2x)dx − π 4log2. After a change of variables, this can be rearranged to get the result.
Why is sin (x^2) not integrable?
Originally Answered: Why sin (x^2) is not integrable? There are a few different ways you can interpret the question. 1. You can say a function on the real numbers is integrable if the definite integral exists. In the case of this function, this integral clearly diverges.
What is the antiderivative of ∫ log(SiNx)DX?
Motivation: Since log(sinx) ′ = cotx, the antiderivative ∫ log(sinx)dx has the nice property F ″ (x) = cotx. Can we find F explicitly? Failing that, can we find the definite integral over one of intervals where log(sinx) is defined?