If \( y=f(x) \) and \( y=g(x) \) are symmetrical about the line \( x=\frac{\alpha+\beta}{2} \), ...

Channel:
Subscribers:
445,000
Published on ● Video Link: https://www.youtube.com/watch?v=uky8sG_XJHI



Category:
Let's Play
Duration: 6:30
1 views
0


If \( y=f(x) \) and \( y=g(x) \) are symmetrical about the line \( x=\frac{\alpha+\beta}{2} \), then \( \int_{\alpha}^{\beta} f(x) g^{\prime}(x) d x \) is equal
(a) \( \int_{\alpha}^{\beta} f^{\prime}(x) g(x) d x \)
(b) \( -\int_{\alpha}^{\beta} f^{\prime}(x) g(x) d x \)
(c) \( \frac{1}{2} \int_{\alpha}^{\beta}\left(f(x) g^{\prime}(x)-f^{\prime}(x) g(x)\right) d x \)
(d) \( \frac{1}{2} \int_{\alpha}^{\beta}\left(f(x) g^{\prime}(x)+f^{\prime}(x) g(x)\right) d x \)
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live




Other Videos By PW Solutions


2023-06-09If \( \lim _{n \rightarrow \infty} \frac{\left[1^{3}+2^{3}+3^{3} \ldots . .+(2 n)^{3}\right] \cd...
2023-06-09Let \( f \) be a real-valued function defined on the interval \( (0, \infty) \) by \( f(x)=\ln x...
2023-06-09\( I=\int_{\pi / 4}^{2 n \pi+\frac{\pi}{4}} \frac{d x}{\left(1+\pi^{\cos x}\right)\left(1+\pi^{\...
2023-06-09Let \( f(x)=\left\{\begin{array}{ll}x+1, & 0 \leq x \leq 1 \\ 2 x^{2}-6 x+6, & 1x \leq 2\end{arr...
2023-06-09If \( \lim _{n \rightarrow \infty}\left(\frac{{ }^{3 n} C_{n}}{{ }^{2 n} C_{n}}\right)^{1 / n}=\...
2023-06-09If \( \int_{0}^{\infty} e^{-x^{2}} d x=\frac{\sqrt{\pi}}{2} \) then match the following Column-I...
2023-06-09Consider a parabola \( y=\frac{x^{2}}{4} \) and the point \( F(0,1) \). Let \( A_{1}\left(x_{1},...
2023-06-09Suppose that the function \( f, g, f^{\prime} \) and \( g^{\prime} \) are continuous over \( [0,...
2023-06-09If \( U_{n}=\int_{0}^{\frac{\pi}{2}} \cos ^{n} x \cos n x d x \) then (a) \( U_{1}, U_{2} \ldots...
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 \( I_{n}=\int_{-n}^{n}\left(\{x+1\}\left\{x^{2}+2\right\}+\left\{x^{2}+3\right\}\left\{x^{3}+...