The area of region bounded by the curves \( 4y=\ x^3,y=0 \) and \( x=4 \) in the first quadrant is :
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 16 sq units
The region lies under the curve \( y=\frac{x^3}{4} \) from x = 0 to x = 4.
\( \displaystyle \text{Area}=\int_0^4\frac{x^3}{4}\,dx \)
\( \displaystyle =\frac{1}{4}\left[\frac{x^4}{4}\right]_0^4 \)
\( \displaystyle =\frac{256}{16} \)
\( \displaystyle =16\ \text{sq units} \)