KCET · Maths · Area Under Curves
The area of the region bounded by the curve \(y=x^2\) and the line \(y=16\) is
- A \(\frac{32}{3}\) sq. units
- B \(\frac{256}{3}\) sq. units
- C \(\frac{64}{3}\) sq. units
- D \(\frac{128}{3}\) sq. units
Answer & Solution
Correct Answer
(B) \(\frac{256}{3}\) sq. units
Step-by-step Solution
Detailed explanation
\(y=x^2, y=16\)
\(\begin{aligned} & 2 \int_0^{16} \sqrt{y} d y=2 \frac{y^{3 / 2}}{3 / 2} \\ & =\frac{4}{3}\left(4^3\right)=\frac{256}{3}\end{aligned}\)
\(\begin{aligned} & 2 \int_0^{16} \sqrt{y} d y=2 \frac{y^{3 / 2}}{3 / 2} \\ & =\frac{4}{3}\left(4^3\right)=\frac{256}{3}\end{aligned}\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- The function \(f(x)=\frac{\log (1+a x)-\log (1-b x)}{x}\) is not defined at \(\mathrm{x}=0\). The value which should be assigned to \(\mathrm{f}\) at \(\mathrm{x}=0\) so that it is continuous at \(\mathrm{x}=0\) isKCET 2009 Easy
- The area bounded by the curve \(x=4-y^{2}\) and the \(Y\)-axis isKCET 2007 Hard
- The distance between the foci of a hyperbola is 16 and its eccentricity is \(\sqrt{2}\). Its equation isKCET 2023 Easy
- If \(y=\sin x \cdot \sin 2 x \cdot \sin 3 x \ldots \sin n x\), then \(y^{\prime}\) isKCET 2011 Medium
- If \( \tan x=\frac{3}{4}, \Pi < x < \frac{3 \Pi}{2} \), then the value of \( \cos \frac{x}{2} \) isKCET 2014 Medium
- \(\frac{d}{d x}\left[\cos ^2\left(\cot ^{-1} \sqrt{\frac{2+x}{2-x}}\right)\right]\) isKCET 2024 Hard
More PYQs from KCET
- A slit of width \(a\) is illuminated by red light of wavelength \(6500 Å\). If the first diffraction minimum falls at \(30^{\circ}\), then the value of \(a\) isKCET 2021 Easy
- For the equilibrium :
\( \mathrm{CaCO}_{3}(s) \rightleftharpoons \mathrm{CaO}(s)+\mathrm{CO}_{2}(g) ; \mathrm{K}_{p}=1.64 \mathrm{~atm} \)
at \( 1000 \mathrm{~K} \)
\( 50 \mathrm{~g} \) of \( \mathrm{CaCO}_{3} \) in a \( 10 \) litre closed vessel is heated to \( 1000 \mathrm{~K} \). Percentage of \( \mathrm{CaCO}_{3} \) that
remains unreacted at equilibrium is
(Given \( \mathrm{R}=0.082 \mathrm{~L} \mathrm{~atm} K^{-1} \mathrm{~mol}^{-1} \) )KCET 2014 Medium - In an alkaline medium, glycine predominantly exists as/in a/anKCET 2011 Easy
- What range of electromagnetic spectrum is considered as light?KCET 2026 Easy
- If \( \left(\frac{1+i}{1-i}\right)^{\mathrm{m}} \), then the least positive integralvalue of \( \mathrm{m} \) isKCET 2017 Easy
- If lines represented by \(x+3 y-6=0\), \(2 x+y-4=0\) and \(k x-3 y+1=0\) are concurrent, then the value of \(k\) isKCET 2011 Easy