COMEDK · Maths · 31. Area Under Curves
Area bounded by the curve \(y=x^{3}\), the \(X\)-axis and the ordinates at \(x=-2\) and \(x=1\), is
- A \(-9\) sq units
- B \(-\frac{15}{4}\) sq units
- C \(\frac{15}{4}\) sq units
- D \(\frac{17}{4}\) sq units
Answer & Solution
Correct Answer
(D) \(\frac{17}{4}\) sq units
Step-by-step Solution
Detailed explanation
\(\begin{aligned} \text { Required area } &=\left|\int_{-2}^{0} x^{3} d x\right|+\int_{0}^{1} x^{3} d x \\ &=\left|\left[\frac{x^{4}}{4}\right]_{-2}^{0}\right|+\left[\frac{x^{4}}{4}\right]_{0}^{1}=\frac{16}{4}+\frac{1}{4}=\frac{17}{4} \text { squnits } \end{aligned}\)
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
- A solid S is made from a cylinder surmounted by a hemisphere on top with both its circular faces sharing a common centre. The radius of cylinder and radius of hemisphere are \(x \mathrm{~cm}\). The height of the cylinder is \((20-4 x) \mathrm{cm}\) and the volume of S is \(V=\dfrac{1}{3} \pi y\). Find the maximum value of \(y\).COMEDK 2025 Medium
- The locus of the point which moves such that the ratio of its distances from two fixed points in the plane is always a constant \(k( < 1)\) isCOMEDK 2016 Easy
- If matrix \(A=\left[\begin{array}{cc}2 & -2 \\ -2 & 2\end{array}\right]\) and \(A^{2}=p A\), then the value of \(p\) isCOMEDK 2021 Medium
- What will be the equation of circle whose centre is \((1,2)\) and touches \(X\) - axis?COMEDK 2021 Medium
- The total number of terms in the expansion of \((x+y)^{60}+(x-y)^{60}\) isCOMEDK 2023 Easy
- \(\int_0^\pi \dfrac{e^{\cos x}}{e^{\cos x}+e^{-\cos x}} d x\) is equal toCOMEDK 2025 Medium
More PYQs from COMEDK
- The circles \(a x^{2}+a y^{2}+2 g_{1} x+2 f_{1} y+c_{1}=0\) and \(b x^{2}+b y^{2}+2 g_{2} x+2 f_{2} y+c_{2}=0\) \((a \neq 0\) and \(b \neq 0)\) cut orthogonally ifCOMEDK 2016 Medium
- If \(A=\{a, b, c\}, B=\{b, c, d\}\) and \(C=\{a, d, c\}\), then \((A-B) \times(B \cap C)=\)COMEDK 2016 Easy
- The spectrum obtained from the chromosphere of the sun at the time of total solar eclipse isCOMEDK 2013 Medium
- A Nitrogen containing organic compound with molecular formula C\(_3\)H\(_5\)N undergoes the following reactions.
C\(_3\)H\(_5\)N + Na / Hg in C\(_2\)H\(_5\)OH \(\rightarrow\) [A]
[A] + CH\(_3\)COCl / NaOH (aq) \(\rightarrow\) [B]
[A] + CHCl\(_3\) / KOH on heating \(\rightarrow\) [C] (foul smelling compound)
Identify compounds [B] and [C]COMEDK 2026 Medium - Which metal has a greater tendency to form metal oxide?COMEDK 2017 Easy
- A galvanometer having a resistance of \(50 \Omega\) is shunted by a wire of resistance \(10 \Omega\). If the total current is 2 A , the current passing through the shunt is:COMEDK 2025 Medium