2024年12月16日 · Ex 7.10, 8 By using the properties of definite integrals, evaluate the integrals : ∫_0^ (𝜋/4) log⁡ (1+tan⁡𝑥 ) 𝑑𝑥 Let I=∫_0^ (𝜋/4) log⁡〖 (1+tan⁡𝑥 )〗 𝑑𝑥 ∴ I=∫_0^ (𝜋/4) log⁡ [1+𝐭𝐚𝐧⁡ (𝝅/𝟒−𝒙) ] 𝑑𝑥 I=∫_0^ (𝜋/4) log⁡ [1+ (tan⁡ 𝜋/4 −tan⁡𝑥)/ (1 +〖 tan ...

2020年3月27日 · I tried to find Maclaurin's expansion for $\log (1 + \tan x)$ by algebraic method as below but coefficients of $x^6$ and $x^7$ are not matching what is given in Mathematica. What did I do wrong? I...

Integration of log (1 + tan x) from 0 to pi/4 is equal to π/8 log 2. Since, this is a definite integral, to integrate it we have to use the propertiesies of definite integrals.

2018年5月17日 · Evaluate:∫log (1+tanx)dx for x→0,π/4.

Differentiate tan − 1 (− x + x) with respect to if 1 −, if − 1 <x <1 ? If and y f (0) = f (1) = 0, f ′ (1) = 2 and y = f (e x) e f (x) write the value of at x d y d x at x = 0 ?

The correct option is A π 8loge2 Let I = ∫ π/4 0 log(1+tanx)dx.....(i) ⇒ I =∫ π/4 0 log[1+tan(π 4−x)]dx [∵ ∫a 0 f (x)dx =∫a 0 f (a−x)dx] = ∫ π/4 0 log[1+ 1−tanx 1+tanx]dx = ∫ π/4 0 log[2 …

2023年1月21日 · Split the range and utilize the known integral I = ∫π 40ln(1 + tanx)dx + ∫π 2π 4ln(1 + tanx)x → π 2 − x dx = 2∫π 40ln(1 + tanx)dx − ∫π 40ln(tanx)dx = π 4ln2 + G

asked Jan 29, 2019 in Mathematics by Aesha (52.5k points) edited Jan 29, 2019 by Aesha

2024年2月6日 · To calculate the definite integral of log(tanx) log (tan x) from (0) to π/2 π / 2, we use a technique involving symmetry and the properties of logarithms. The integral is: ∫ π/2 0 …

∴ ∫ 0 π 4 log (1 + tan x) d x = π 8 log 2. Fundamental Theorem of Integral Calculus. Is there an error in this question or solution? Solve the following.