If \( f(x) \) is a periodic function with period 3 and defind as \( f(x)\left\{\begin{array}{ll}... VIDEO
If \( f(x) \) is a periodic function with period 3 and defind as \( f(x)\left\{\begin{array}{ll}\{x\}, & x \in(0,1) \\ {[x],} & x \in(1,2) \\ \{-x\}, & x \in(2,3)\end{array}\right. \) then the value of \( \frac{1}{3} \int_{3}^{12} f(x) d x \) (where [.] and \( \{ \).\( \} denote greatest integer and fractional part \) functions, respetively)
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live
Other Videos By PW Solutions 2023-06-09 Let \( C_{1} \& C_{2} \) be two curves passing through the origin as shown in the figure. A curv... 2023-06-09 \[
\text { If } f(x)=\sin x, \forall x \in\left[0, \frac{\pi}{2}\right], f(x)+f(\pi-x)=2, \foral... 2023-06-09 Find the area of a loop as well as whole area of the curve \( a^{2} y^{2}=x^{2}\left(a^{2}-x^{2}... 2023-06-09 The ratio of the areas of two regions of the curve \( C_{1}: 4 x^{2}+ \) \( \pi^{2} y^{2}=4 \pi^... 2023-06-09 The parabola \( P: y=a x^{2} \) where \( a \) is a positive real constant, is touched by the l... 2023-06-09 Match the following:
\begin{tabular}{|l|l|c|l|}
\hline \multicolumn{2}{|c|}{ Column-I } & \multi... 2023-06-09 The area eaclosed by \( g(x), x=-3, x=5 \) and \( x \)-axis where \( g(x) \) is the inverse of \... 2023-06-09 If \( y=g(x) \) is the inverse of a bijective mapping \( f: R \rightarrow R \), \( f(x)=6 x^{5}+... 2023-06-09 Let \( A(k) \) be the area bounded by the cuerves \( y=x^{2}-3 \) and \( y=k x+2 \)
(a) The rang... 2023-06-09 Consider the areas \( S_{0}, S_{1}, S_{2}, \ldots \). bounded by the \( x \)-axis and half-waves... 2023-06-09 If \( f(x) \) is a periodic function with period 3 and defind as \( f(x)\left\{\begin{array}{ll}... 2023-06-09 Let \( C \) be a curve passing through \( M(2,2) \) such that the slope of the tangent at any po... 2023-06-09 The value of \( a(a0) \) for which the area bounded by curves \( y=\frac{x}{6}+\frac{1}{x^{2}}, ... 2023-06-09 The figure shows a horizontal line \( y=c \) passing through \( (b, c) \) intersecting the curve... 2023-06-09 Consider the following regions in the plane:
\[
\begin{array}{l}
A=\left\{(x, y): y^{2}=4[\sqrt{... 2023-06-09 If area of ellipse \( 2 x^{2}+6 x y+5 y^{2}=1 \) is \( \mathrm{A} \)
Statement-I: A is between t... 2023-06-09 Find the value(s) of the parameter \( a \) \( (a0) \) for each of which the area of the figure... 2023-06-09 Find the area bounded by \( y=x+\sin x \) and its inverse between \( x=0 \) and \( x=2 \pi \).
(... 2023-06-09 Let \( f(x)=\left\{\begin{array}{cc}2 x, & 0 \leq x \leq 1 \\ 2, & 1 \leq x \leq 3 \\ 8-2 x, & 3... 2023-06-09 \begin{tabular}{|l|l|c|c|}
\multicolumn{2}{|c|}{ Let \( f(x)=|x|, g(x)=|x-1| \) and \( h(x)=|x+1... 2023-06-09 Find the ratio in which the area bounded by the curves \( y^{2}=12 x \) and \( x^{2}=12 y \) is ...