Match the entries of Column-I with those of Column-II.
\begin{tabular}{|l|l|l|l|}
\hline \multic....
Match the entries of Column-I with those of Column-II.
\begin{tabular}{|l|l|l|l|}
\hline \multicolumn{2}{|c|}{ Column-I } & \multicolumn{2}{c|}{ Column-II } \\
\hline (A) & \( \int e^{x} \frac{\left(x^{3}+x+1\right)}{\left(1+x^{2}\right)^{3 / 2}} d x \) & (p) & \( e^{x}\left(\frac{x+1}{x+2}\right)+c \) \\
\hline (B) & \( \int \frac{e^{x}\left(x^{3}-x+2\right)}{\left(x^{2}+1\right)^{2}} d x \) & (q) & \( \frac{e^{x}}{1+x^{2}}+c \) \\
\hline (C) & \( \int e^{x}\left[\frac{1-x}{1+x^{2}}\right]^{2} d x \) & (r) & \( \frac{e^{x} x}{\sqrt{1+x^{2}}}+c \) \\
\hline (D) & \( \int e^{x} \frac{\left(x^{2}+3 x+3\right)}{(x+2)^{2}} d x \) & (s) & \( \frac{e^{x}(x+1)}{x^{2}+1}+c \) \\
\hline
\end{tabular}
(1) (A) \( \rightarrow \) (r), (B) \( \rightarrow \) (q), (C) \( \rightarrow \) (s), (D) \( \rightarrow \) (p)
(2) (A) \( \rightarrow(\mathrm{r}),(\mathrm{B}) \rightarrow(\mathrm{s}),(\mathrm{C}) \rightarrow(\mathrm{q}),(\mathrm{D}) \rightarrow(\mathrm{p}) \)
(3) (A) \( \rightarrow \) (q), (B) \( \rightarrow(\mathrm{r}),(\mathrm{C}) \rightarrow(\mathrm{p}),(\mathrm{D}) \rightarrow(\mathrm{s}) \)
(4) (A) \( \rightarrow(\mathrm{q}),(\mathrm{B}) \rightarrow(\mathrm{r}),(\mathrm{C}) \rightarrow(\mathrm{s}),(\mathrm{D}) \rightarrow(\mathrm{p}) \)
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live
Other Videos By PW Solutions
2024-01-22 | Let \( A(k) \) be the area bounded by the curves
\( y=x^{2}+2 x-3 \) and \( y=k x+1 \). Then.... |
2024-01-22 | Consider the two curves \( c_{1}: y=1+\cos x \) and
\( c_{2}: y=1+\cos (x-\alpha) \) for \( \alp.... |
2024-01-22 | The integrating factor of the differential equation
\( \frac{d y}{d x}=y \tan x-y^{2} \sec x \),.... |
2024-01-22 | The solution of \( \frac{d y}{d x}+2 y \tan x=\sin x \), is.... |
2024-01-22 | The area of the region bounded by the curve
\( y=\sqrt{5-x^{2}} \) and \( y=|x-1| \), is.... |
2024-01-22 | The solution of the differential equation,
\( y d x+\left(x+x^{2} y\right) d y=0 \) is.... |
2024-01-22 | If the curve \( y=a x^{\frac{1}{2}}+b x \) passes through the point
\( (1,2) \) and lies above t.... |
2024-01-22 | The area bounded by \( y=x^{2} \) and \( y=x^{\frac{1}{3}} \) for
\( x \in[-1,1] \) is
W..... |
2024-01-22 | The area of bounded by the curve \( y=x^{2} \) and
\( y=\frac{2}{1+x^{2}} \), is.... |
2024-01-22 | The area of bounded by the curve \( x^{2}=4 y \) and the
straight line \( x=4 y-2 \), is.... |
2024-01-22 | Match the entries of Column-I with those of Column-II.
\begin{tabular}{|l|l|l|l|}
\hline \multic.... |
2024-01-22 | The area bounded by the parabolas
\( x=-2 y^{2}, x=1-3 y^{2} \) is.... |
2024-01-22 | The area bounded by the parabola \( y=x^{2}+1 \) and
the straight line \( x+y=3 \), is.... |
2024-01-22 | The area bounded by the curves \( y=\sin x \) and \( y= \)
\( \cos x \) between two consecutive .... |
2024-01-22 | The area bounded by the curve \( x y^{2}=4(2-x) \) and
\( y \)-axis, is.... |
2024-01-22 | If \( \int \frac{\cot ^{3} x \cos x}{\left(\sin ^{5} x+\cos ^{5} x\right)^{3 / 5}} d x=\frac{-1}.... |
2024-01-22 | The area bounded by the curve \( y=(x-1)(x-2) \)
\( (x-3) \) lying between the ordinates \( x=1 .... |
2024-01-22 | \( \int \frac{4 e^{x}+6 e^{-x}}{9 e^{x}-4 e^{-x}} d x \) equals.... |
2024-01-22 | The area bounded by the curve \( y=\sin ^{-1} x \) and the
lines \( x=0,|y|=\frac{\pi}{2} \), is.... |
2024-01-22 | The area enclosed by the curves \( x^{2}=y, y=x+2 \),
and \( x \)-axis, is.... |
2024-01-22 | The area of bounded by \( x=2 y-y^{2} \) and the \( y \)-axis
is.... |