Let \( I_{1}=\int_{0}^{\infty} \frac{x^{2} \sqrt{x}}{(1+x)^{6}} d x, I_{2}=\int_{0}^{\infty} \fr...
Let \( I_{1}=\int_{0}^{\infty} \frac{x^{2} \sqrt{x}}{(1+x)^{6}} d x, I_{2}=\int_{0}^{\infty} \frac{x \sqrt{x}}{(1+x)^{6}} d x \), then
(a) \( I_{1}=2 I_{2} \)
(b) \( I_{2}=2 I_{1} \)
(c) \( I_{1}=I_{2}^{2} \)
(d) \( I_{1}=I_{2} \)
š²PW App Link - https://bit.ly/YTAI_PWAP
šPW Website - https://www.pw.live
Other Videos By PW Solutions
| 2023-06-09 | Let \( f(x)=\left\{\begin{array}{ll}x+1, & 0 \leq x \leq 1 \\ 2 x^{2}-6 x+6, & 1x \leq 2\end{arr... |
| 2023-06-09 | If \( \lim _{n \rightarrow \infty}\left(\frac{{ }^{3 n} C_{n}}{{ }^{2 n} C_{n}}\right)^{1 / n}=\... |
| 2023-06-09 | If \( \int_{0}^{\infty} e^{-x^{2}} d x=\frac{\sqrt{\pi}}{2} \) then match the following Column-I... |
| 2023-06-09 | Consider a parabola \( y=\frac{x^{2}}{4} \) and the point \( F(0,1) \).
Let \( A_{1}\left(x_{1},... |
| 2023-06-09 | Suppose that the function \( f, g, f^{\prime} \) and \( g^{\prime} \) are continuous over \( [0,... |
| 2023-06-09 | If \( U_{n}=\int_{0}^{\frac{\pi}{2}} \cos ^{n} x \cos n x d x \) then
(a) \( U_{1}, U_{2} \ldots... |
| 2023-06-09 | If \( \int_{0}^{1}\left(\sum_{k=1}^{2014} \frac{x^{2}}{x^{3}+k^{3}}\right)\left(\prod_{k=1}^{201... |
| 2023-06-09 | If \( y=f(x) \) 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}{... |
| 2023-06-09 | Let \( f:[0,1] \rightarrow[0, \infty) \) be a continuous function such that \( \int_{0}^{1} f(x)... |
| 2023-06-09 | Let \( 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[... |
| 2023-06-09 | Let \( I(n)=\int_{2016}^{2016+\frac{1}{n}} x \cos ^{2}(x-2016) d x \)
Statement 1: \( I\left(\fr... |
| 2023-06-09 | Evaluate: \( \int_{0}^{\infty}\left(\frac{\tan ^{-1} x}{x}\right)^{3} d x \) |
| 2023-06-09 | If \( I_{1}=\int_{0}^{1} \frac{1+x^{8}}{1+x^{4}} d x \) and \( I_{2}=\int_{0}^{1} \frac{1+x^{9}}... |
| 2023-06-09 | If \( a, b \) can \( c \) are real numbers, then the value of \( \lim _{t \rightarrow 0} \ln \le... |
| 2023-06-09 | If \( \int_{0}^{\sin ^{-1} \pi / 4}(\pi-4 \sin \theta) \sin 2 \theta \ln (1+\tan (\sin \theta)) ... |
| 2023-06-09 | If \( I_{n}=\int_{-n}^{n}\left(\{x+1\}\left\{x^{2}+2\right\}+\left\{x^{2}+3\right\}\left\{x^{3}+... |
| 2023-06-09 | If \( f(x)=x^{5}+5 x-1 \) then \( \int_{5}^{41} \frac{d x}{\left(f^{-1}(x)\right)^{5}+5 f^{-1}(x... |
| 2023-06-09 | If \( \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... |
0