If \( \int_{0}^{\sin ^{-1} \pi / 4}(\pi-4 \sin \theta) \sin 2 \theta \ln (1+\tan (\sin \theta)) ...

Channel:
PW Solutions
Subscribers:
445,000
Published on ● Video Link: https://www.youtube.com/watch?v=6fd9zCPjqVk


Duration: 10:05
1 views
0

If \( \int_{0}^{\sin ^{-1} \pi / 4}(\pi-4 \sin \theta) \sin 2 \theta \ln (1+\tan (\sin \theta)) d \theta \) is \( k \) then \( \frac{960 k}{\pi^{3} \ln 2} \) is equal to
(a) 11
(b) 10
(c) 12
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live



Other Videos By PW Solutions


2023-06-09If \( \int_{0}^{1}\left(\sum_{k=1}^{2014} \frac{x^{2}}{x^{3}+k^{3}}\right)\left(\prod_{k=1}^{201...
2023-06-09If \( y=f(x) \) and \( y=g(x) \) are symmetrical about the line \( x=\frac{\alpha+\beta}{2} \), ...
2023-06-09\( \int_{-1}^{1}\left(e^{x^{3}}+e^{-x^{3}}\right) d x \) is less then (a) 2 (b) \( 2 e+\frac{2}{...
2023-06-09Let \( f:[0,1] \rightarrow[0, \infty) \) be a continuous function such that \( \int_{0}^{1} f(x)...
2023-06-09Let \( I_{1}=\int_{0}^{\infty} \frac{x^{2} \sqrt{x}}{(1+x)^{6}} d x, I_{2}=\int_{0}^{\infty} \fr...
2023-06-09\[ \int_{-4}^{4} \frac{\sin ^{-1}(\sin x)+\cos ^{-1}(\cos x)}{\left(1+x^{2}\right)\left(1+\left[...
2023-06-09Let \( I(n)=\int_{2016}^{2016+\frac{1}{n}} x \cos ^{2}(x-2016) d x \) Statement 1: \( I\left(\fr...
2023-06-09Evaluate: \( \int_{0}^{\infty}\left(\frac{\tan ^{-1} x}{x}\right)^{3} d x \)
2023-06-09If \( I_{1}=\int_{0}^{1} \frac{1+x^{8}}{1+x^{4}} d x \) and \( I_{2}=\int_{0}^{1} \frac{1+x^{9}}...
2023-06-09If \( a, b \) can \( c \) are real numbers, then the value of \( \lim _{t \rightarrow 0} \ln \le...
2023-06-09If \( \int_{0}^{\sin ^{-1} \pi / 4}(\pi-4 \sin \theta) \sin 2 \theta \ln (1+\tan (\sin \theta)) ...
2023-06-09If \( f(x)=x^{5}+5 x-1 \) then \( \int_{5}^{41} \frac{d x}{\left(f^{-1}(x)\right)^{5}+5 f^{-1}(x...
2023-06-09If \( \int_{-20}^{-10}\left(\frac{x^{2}-x}{x^{3}-3 x+1}\right)^{2} d x+\int_{\frac{1}{21}}^{\fra...
2023-06-09\( S_{1}: \) If \( n \) is a positive integer then \[ \begin{array}{l} \int_{0}^{n \pi}\left|\fr...
2023-06-09The value of \( \int_{0}^{I}\left(\prod_{r=1}^{n}(x+r)\right)\left(\sum_{k=1}^{n} \frac{1}{x+k}\...
2023-06-09Evaluate: \( I=\int_{0}^{1} \frac{\tan ^{-1} a x}{x \sqrt{1-x^{2}}} d x \)
2023-06-09\[ \text { If } \begin{array}{l} \int_{0}^{1}\left(\sum_{r=1}^{2013} \frac{x}{x^{2}+r^{2}}\righ...
2023-06-09If \( f(x)=\int_{0}^{1} e^{|t-x|} d t \) where \( (0 \leq x \leq 1) \), then maximum value of \(...
2023-06-09Match the following Column-I with Column-II \begin{tabular}{|l|l|l|l|} \hline \multicolumn{2}{|c...
2023-06-09\( \lim _{x \rightarrow 0} \frac{\int_{0}^{x^{2}}\left(\tan ^{-1} t\right)^{2} d t}{\int_{0}^{x^...
2023-06-09\[ \int_{a}^{b} x^{n-1} \frac{\left((n-2) x^{2}+(n-1)(a+b) x+n a b\right)}{(x+a)^{2}(x+b)^{2}} d...