Area Under the Curve — Class 12 Mathematics PYQs

Direction : Consider the following for the two (02) items that follow :

The area bounded by the parabola $y^2=kx$ and the line $x=k$, where $k>0$, is $4/3$ square units.

What is the value of $k$?

Consider the following for the next two (02) items that follow:

The circle $x^2+y^2-2x=0$ is partitioned by line $y=x$ in two segments. Let $A_1,A_2$ be the areas of major and minor segments respectively.

What is the value of $A_1$?

Consider the following for the next two (02) items that follow:

The circle $x^2+y^2-2x=0$ is partitioned by line $y=x$ in two segments. Let $A_1,A_2$ be the areas of major and minor segments respectively.

What is the value of $\frac{2(A_1+A_2)}{A_1-3A_2}$?

Consider the following for the next two (02) items that follow :

The line $y=x$ partitions the circle $(x-a{)}^2+y^2=a^2$ in two segments.

What is the area of minor segment?

Consider the following for the next two (02) items that follow :

The line $y=x$ partitions the circle $(x-a{)}^2+y^2=a^2$ in two segments.

What is the area of major segment?

What is the area between the curve $f(x)=x|x|$ and x-axis for $x\in [-1,1]$ ?

For what value of $m$ with $m<0$, is the area bounded by the lines $y=x,y=mx$ and $x=2$ equal to $3$?

The area of the region bounded by the parabola $y^2=4kx$, where $k>0$ and its latus rectum is $24$ square units. What is the value of $k$ ?

What is the area included in the first quadrant between the curves $y=x$ and $y=x^3$ ?

What is the area bounded by $y=\sqrt{16-x^2}$, $y\ge 0$ and the x-axis?