Class 12

Math

Calculus

Area

Area enclosed by the curve $y=f(x)$ defined parametrically as $x=1+t_{2}1−t_{2} ,y=1+t_{2}2t $ is equal to

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The area in the first quadrant between $x_{2}+y_{2}=π_{2}$ and $y=sinx$ is

Find the area enclosed by the figure described by the equation $x_{4}+1=2x_{2}+y_{2}.$

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

Area of the region bounded by the curve $y=e_{x_{2}}$ and the line y=e is

Let R be the region containing the point (x, y) on the X-Y plane, satisfying $2≤∣x+3y∣+∣x−y∣≤4.$ Then the area of this region is

Let A(k) be the area bounded by the curves $y=x_{2}−3$ and y=kx+2\displaystyle.

Consider curves $y=x_{2}1 ,y=4(x−1)1 .Letα$ be the value of $a(a>2)$ for which area bounded by curves between $x=2andx=ais1/aise_{2}+1andβbe the ofb∈(1,2),$ for which the area bounded by curves between x=b and $x=2is1−b1 ,$ then

Find the area of the region bounded by the curves $y=x+2 andy=x+11 $ between the lines x=0 and x=2.