Area Under the Curve — NDA Mathematics PYQs

Consider the following for the two (02) items that follow :
The slope of the tangent to the curve $y=f(x)$ at $(x,f(x))$ is $4$ for every real number $x$ and the curve passes through the origin.

What is the area bounded by the curve, the $x$-axis and the line $x=4$?

Consider the following for the two (02) items that follow :
Let the curve $f(x)=|x-3|$.

What is the area bounded by the curve $f(x)$ and $y=3$?

Consider the following for the two (02) items that follow :
Let the function $f(x)=x^2-1$.

What is the area bounded by the function $f(x)$ and the $x$-axis?

Consider the following for the three (03) items that follow :
Consider the function $f(x)=x|x|$.

What is the area bounded by the curve $f(x)$, the $x$-axis and the lines $x=-2$ and $x=1$?

What is the area of the region bounded by $|x|\le 2k$ and $|y|\le k$, where $k$ is a positive real number?