MHT CET · Maths · Definite Integration

The value of \(\int_{\frac{1}{3}}^1\left(x-x^3\right)^{\frac{1}{3}} \mathrm{~d} x\) is

A \(0\)
B \(2\)
C \(4\)
D \(6\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(0\)

Step-by-step Solution

Detailed explanation

No Solution

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

If the mean and variance of a binomial distribution are 4 and 2 respectively, then probability of getting 2 heads is

MHT CET 2021 Hard
If \(y=\log _{\sin x} \tan x\), then \(\left(\frac{\mathrm{d} y}{\mathrm{~d} x}\right)_{x=\frac{\pi}{4}}\) has the value

MHT CET 2023 Medium
The product of the perpendicular distances from \((2,-1)\) to the pair of lines \(2 x^2-5 x y+2 y^2=0\) is

MHT CET 2021 Medium
\(\int \frac{\mathrm{d} x}{\cos x(1+\cos x)}=\)

MHT CET 2025 Medium
In a triangle \(\mathrm{ABC}\), with usual notations, if \(\mathrm{c}=4\), then value of \((a-b)^2 \cos ^2 \frac{C}{2}+(a+b)^2 \sin ^2 \frac{C}{2}\) is

MHT CET 2023 Hard
The value of \(\cos \left(\tan ^{-1}\left(\sin \left(\cot ^{-1} x\right)\right)\right)\) is

MHT CET 2022 Medium

Explore more questions on app

From MHT CET

In a resonance tube the first resonance with a tunning fork occurs at \(16 \mathrm{~cm}\) and second at \(49 \mathrm{~cm} .\) If the velocity of sound is \(330 \mathrm{~m} / \mathrm{s}\), the frequency of tunning fork is

MHT CET 2011 Hard
The unit vector perpendicular to each of the vectors \(\bar{a}+\bar{b}\) and \(\bar{a}-\bar{b}\), where \(\bar{a}=\hat{i}+\hat{j}+\hat{k}\) and \(\overline{\mathrm{b}}=3 \hat{\mathrm{i}}-2 \hat{\mathrm{j}}+5 \hat{\mathrm{k}}\) is

MHT CET 2023 Easy
A wire has three different sections as shown in figure. The magnitude of the magnetic field produced at the centre ' 0 ' of the semicircle by three sections together is ( \(\mu_0=\) permiability of free space)

MHT CET 2025 Medium
A car sounding a horn of frequency \(1000 \mathrm{~Hz}\) passes an observer. The ratio of frequencies of the both noted by the observer before and after passing of the car is 11:9. If the speed of sound is \(V\), the speed of the car is

MHT CET 2022 Easy
If amplitude of \((z-2-3 i)\) is \(\frac{3 \pi}{4}\), then locus of \(z\) is (where \(\mathrm{z}=\mathrm{x}+\) iy)

MHT CET 2021 Medium
A photosensitive surface has work function \(\phi\). If photon of energy \(3 \phi\) falls on this surface, the electron comes out with maximum velocity of \(4 \times 10^6 \mathrm{~m} / \mathrm{s}\). When photon energy is increased to \(7 \phi\) then maximum velocity of photoelectron will be

MHT CET 2025 Medium

Explore more questions on app