The Problem of Areas

Q. Find the area of the region bounded by $y=x^3,y=0,x=2$ and $x=4$.

1. 64
2. 60
3. 16
4. 256

Q. If $x=(3y^2+4y+3)$, then $\int xdy$ will be

1. $3y^2+4y+3+C$
2. $3y^2+8y+3+C$
3. $y^3+2y^2+3y+C$
4. $3y^3+4y+6+C$

Q. Find the area of the region bounded by $y=x^3,y=0,x=2$ and $x=4$.

1. 64
2. 60
3. 16
4. 256

Q. The area of the region enclosed by the curves $y=x,x=e,y=\frac{1}{x}$ and the positive x-axis is:-

Q. Find the area of the region bounded by the curve $y^2=4x,x=1$, $x=4$ and the $x$-axis in the first quadrant.

1. $\frac{28}{3}$
2. $4$
3. $\frac{7}{3}$
4. $\frac{4}{3}$