Let i = ∫ 0 π 2 log ( tan x) ⋅ d x. Show activity on this post. From (i) we can substitute the value, we get.
integrate sin2x log(tanx) dx {0 to pi/2} Math
And found this value using the known sum π 2 6.
(a) π/4 (b) π/2 (c) 0 (d) π
Post your answer (best answer will be rewarded with handsome gifts) please login or register for upload image. Integration of log(1 + tan x) from 0 to π/4 is equal to π/8 log 2. Lata in calculus 1 decade ago, total answer(s): If ∫ cos x l o g ( t an 2 x ) d x = s in x l o g ( t an 2 x ) + f(x) then f(x) is equal to, (assuming c is a arbitrary real constant)
I = ∫ 0 π / 4 l o g ( 2 1 + t a n x) d x.
Integral 0 to pi/2 of sin 2x log tanx dx. Dx let us consider log(sinx) = z cosx/sinx = z → ∫zdz = z²/2 + c hope it helps you ! I arrived at this integral while trying different ways to evaluate 1 1 2 + 1 2 2 + 1 3 2 +. ( x) d x = − π 2 24.
It would be better to have a.
On combining the like terms we get. Since, this is a definite integral, to integrate it we have to use the following property of definite integrals. Editor toolbars basic styles bold paragraph insert/remove numbered list insert/remove bulleted list insert image insert horizontal. Let i = \(\int_{0}^{\pi/4}\) log(1 + tan x) dx.
Check answer and solution for above mathema
X^ {\msquare} \log_ {\msquare} \sqrt {\square} \nthroot [\msquare] {\square} \le. Pioneer, 1 decade ago like. If ∫ cos x log(tan (x/2))dx = sin x log(tan (x/2))+ f(x) then f(x) is equal to, (assuming c is a arbitrary real constant) q. Find the value of integrals ∫ π 2 0 log(tanx + cotx)dx ∫ 0 π 2 l o g ( t a n x + c o t x) d x.
Solve the problem in photo showing each step clearly.
1) let x + log(secx) = t 2) on differentiating it with respect to x you get 1+(1/secx*secx.tanx)=dt/dx this has become so because derivative of x w.r.t to x is 1 , derivative of log x is 1/x and chain rule is also used. ∫_0^(𝜋/4) log(1+tan𝑥 ) 𝑑𝑥 let i=∫_0^(𝜋/4) log〖 (1+tan𝑥 )〗 𝑑𝑥 ∴ i=∫_0^(𝜋/4) log[1+tan(𝜋/4−𝑥) ] 𝑑𝑥 i=∫_0^(𝜋/4) log[1+(tan 𝜋/4 −tan𝑥)/(1 +〖 tan〗 𝜋/4. The value of the integral ∫ log tan x dx x ∈ [0,π ⁄ 2] is equal to : = ∫ 0 π 2 log ( cot x) ⋅ d x.
Here, a = π 2.
We will be using a definite integral property for solving this question. Integral of log( sin( x)) tan( x) bookmark this question. Here you will learn proof of integration of tanx or tan x and examples based on it. Ex 7.11, 8 by using the properties of definite integrals, evaluate the integrals :
= ∫ 0 π 2 log ( 1 tan x) ⋅ d x.
The answer is log|x+log(secx)| we perform this integration like this int (1+tanx)/(x+log(secx))dx using substitution method :
