Class 12

Math

Calculus

Area

Consider two curves $C_{1}:y_{2}=4[y ]xandC_{2}:x_{2}=4[x ]y,where[.]$ denotes the greatest integer function. Then the area of region enclosed by these two curves within the square formed by the lines $x=1,y=1,x=4,y=4$ is

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The area bounded by the curves $y=cos_{−1}x,y=sin_{−1}xandy=−πx_{3},$ where $−1≤x≤1$,is

If A is the area bounded by the curves $y=1−x_{2} andy=x_{3}−x,then the value ofπ/A$ is ___.

Consider the function defined implicity by the equation $y_{2}−2ye_{sin_{−1}x}+x_{2}−1+[x]+e_{2sin_{−1}x}=0(where [x] denotes the greatest integer function).$ The area of the region of curve and line $x=0andx=21 $ is

Consider the area $S_{0},S_{1},S_{2}….$ bounded by the x-axis and half-waves of the curve $y=e_{−x}sinx,wherex≥0.$ The sequence $S_{0},S_{1},S_{2},…,$ forms a G.P. with common ratio

Match the following lists :

The area of the region bonded by $y=e_{x},y=e_{−x},x=0$ and x = 1 is

If S is the sum of cubes of possible value of c for which the area of the figure bounded by the curve $y=8x_{2}−x_{5}$, then straight lines x=1 and x=c and the abscissa axis is equal to $16/3$, then the value of [S], where [.] denotes the greatest integer function, is ___.

Consider the function defined implicity by the equation $y_{2}−2ye_{sin_{−1}x}+x_{2}−1+[x]+e_{2sin_{−1}x}=0(where [x] denotes the greatest integer function).$ Line x=0 divides the region mentioned above in two parts. The ratio of area of left-hand side of line to that of right-hand side of line is