MHT CET · Maths · Area Under Curves
The area bounded by the curve \(y=x^{3}\), the \(\mathrm{X}\) -axis and the lines \(x=1\) and \(x=4\) is
- A \(\frac{127}{4}\) sq. units
- B 64 sq. units
- C 27 sq. units
- D \(\frac{255}{4}\) sq. units
Answer & Solution
Correct Answer
(D) \(\frac{255}{4}\) sq. units
Step-by-step Solution
Detailed explanation
Required area is shaded.
\(\begin{aligned}
\text { Area } &=\int_{1}^{4} x^{3} d x=\left[\frac{x^{4}}{4}\right]_{1}^{4} \\
&=\frac{1}{4}\left[4^{4}-1\right]=\frac{1}{4}(256-1)=\frac{255}{4} \text { sq. unit }
\end{aligned}\)
\(\begin{aligned}
\text { Area } &=\int_{1}^{4} x^{3} d x=\left[\frac{x^{4}}{4}\right]_{1}^{4} \\
&=\frac{1}{4}\left[4^{4}-1\right]=\frac{1}{4}(256-1)=\frac{255}{4} \text { sq. unit }
\end{aligned}\)
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