Match the following Column-I with Column-II:
\begin{tabular}{|l|c|c|c|}
\hline & Column-I & & Co...
Match the following Column-I with Column-II:
\begin{tabular}{|l|c|c|c|}
\hline & Column-I & & Column-II \\
\hline A. & \( \int \frac{d x}{\left(a^{2}-x^{2}\right)^{2}}-\frac{1}{2 a^{2}} \) & p. & \( \sqrt{x^{2}-a^{2}}-a \sec ^{-1} \frac{x}{a}+c \) \\
\hline B. & \( \int \frac{d x}{a^{2}-x^{2}} \) is equal to & & \\
\hline C. & \( \int \frac{\sqrt{a^{2}-x^{2}}}{x^{2}} d x \) & q. & \( -\frac{\sqrt{a^{2}-x^{2}}}{x}+\cos ^{-1} \frac{x}{a}+c \) \\
\hline D. & \( \int \frac{\sqrt{x^{2}-a^{2}}}{x} d x \) & r. & \( \frac{\sqrt{x^{2}-a^{2}}}{a^{2} x}+c \) \\
\hline & s. & & \( \frac{x}{2 a^{2}\left(a^{2}-x^{2}\right)}+c \) \\
\hline
\end{tabular}
(a) \( \mathrm{A} \rightarrow \mathrm{p} ; \mathrm{B} \rightarrow \mathrm{r} ; \mathrm{C} \rightarrow \) q; D \( \rightarrow \mathrm{s} \)
(b) \( \mathrm{A} \rightarrow \mathrm{s} \); B \( \rightarrow \) r; \( \mathrm{C} \rightarrow \mathrm{r} ; \mathrm{D} \rightarrow \mathrm{p} \)
(c) \( \mathrm{A} \rightarrow \mathrm{s} \); B \( \rightarrow \) p; C \( \rightarrow \) q; D \( \rightarrow \mathrm{p} \)
(d) \( \mathrm{A} \rightarrow \mathrm{s} ; \mathrm{B} \rightarrow \mathrm{r} ; \mathrm{C} \rightarrow \mathrm{q} ; \mathrm{D} \rightarrow \mathrm{p} \)
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live
Other Videos By PW Solutions
| 2023-06-09 | The value of \( \int_{0}^{\infty} x^{2 n+1} e^{-x^{2}} d x, n \in N \)
(a) \( n ! \)
(b) \( (n+1... |
| 2023-06-09 | Assume that \( f^{\prime \prime} \) is continuous and that \( f(1)=3, f^{\prime}(1)=2 \) and \( ... |
| 2023-06-09 | Evaluate \( \int \sin ^{-1}\left(\frac{2 x+2}{\sqrt{4 x^{2}+8 x+13}}\right) d x \) |
| 2023-06-09 | Evaluate \( \int\left(x^{3 m}+x^{2 m}+x^{m}\right)\left(2 x^{2 m}+3 x^{m}+6\right)^{1 / m} d x, ... |
| 2023-06-09 | If \( g(x) \) is the inverse of \( f(x) \) and \( f(x) \) has domain \( x \in[1,5] \), where \( ... |
| 2023-06-09 | For \( I(x)=\int \frac{\sec ^{2} x-2022}{\sin ^{2022} x} d x \), if \( I\left(\frac{\pi}{4}\righ... |
| 2023-06-09 | \[
\int_{-\pi / 2}^{\pi / 2} \log \left(\frac{2-\sin \theta}{2+\sin \theta}\right) d \theta=
\]
... |
| 2023-06-09 | Let \( I=\int \frac{e^{x}}{e^{4 x}+e^{2 x}+1} d x, J=\int \frac{e^{-x}}{e^{-4 x}+e^{-2 x}+1} d x... |
| 2023-06-09 | \( \int \frac{\left(1-\frac{1}{\sqrt{3}}\right)(\cos x-\sin x)}{\left(1+\frac{2}{\sqrt{3}} \sin ... |
| 2023-06-09 | Evaluate: \( \int e^{(x \sin x+\cos x)}\left(x \cos x\left(\frac{\cos x}{x}\right)+\left(\frac{\... |
| 2023-06-09 | Match the following Column-I with Column-II:
\begin{tabular}{|l|c|c|c|}
\hline & Column-I & & Co... |
| 2023-06-09 | Evaluate \( \int \frac{d x}{x^{2}\left(x^{4}+1\right)^{3 / 4}} \) |
| 2023-06-09 | \( \frac{\int\left(x^{2}+1\right) e^{x}}{(x+1)^{2}} d x=f(x) e^{x}+C \), Where \( C \) is consta... |
| 2023-06-09 | The value of \( \int e^{x^{2}}(2 x-\cot x)\left(x^{2}-\ln (\sin x)\right)(\operatorname{cosec} x... |
| 2023-06-09 | Evaluate: \( \int \sin 4 x \cdot e^{\tan ^{2} x} d x \) |
| 2023-06-09 | If \( I_{n}=\int(\sin x+\cos x)^{n} d x \) and \( I_{n}=\frac{1}{n}(\sin x+\cos x)^{n-1} \) \( (... |
| 2023-06-09 | Evaluate: \( \int \frac{x^{2}-1}{x \sqrt{x^{4}+4 x^{3}-6 x^{2}+4 x+1}} d x \) |
| 2023-06-09 | If \( I_{m, p}=\int x^{m}\left(a+b x^{n}\right) p \cdot d x \) and \( I_{m, p}=\frac{x^{m+1}\lef... |
| 2023-06-09 | \( \int \frac{e^{x} \sin x \cos x}{(1+\sin x)^{2}(1-\sin x+\cos x)} d x \) is equal to
(a) \( \f... |
| 2023-06-09 | Let \( 4 x^{4}-24 x^{3}+31 x^{2}+6 x-8=0 \) has roots \( \alpha, \beta, \gamma, \delta \), where... |
| 2023-06-09 | Let \( y^{2}=2 x^{2}+4 x+3 \) and \( I_{n}=\int \frac{x^{n}}{y} d x \), then the value of \( a+b... |
0