Question
The changes in a function y and the independent dy variable x are related as $\frac{\text{dy}}{\text{dx}}=\text{x}^2.$ Find y as a function of x.
✓
Answer
The change in a function of y and the independent variable x are related as $\frac{\text{dy}}{\text{dx}}=\text{x}^2.$
$\Rightarrow\text{dy}=\text{x}^2\text{dx}$
Taking integration of both sides,$\int\text{dy}=\int\text{x}^2\text{dx}\Rightarrow\text{y}=\frac{\text{x}^3}{3}+\text{c}$
$\therefore$ y as a function of x is represented by $\text{y}=\frac{\text{x}^3}{3}+\text{c}.$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Find the value of X in the given figure.
Using Rutherford model of the atom, derive the expression for the total energy of the electron in hydrogen atom. What is the significance of total negative energy possessed by the electron?
Two voltameters, one having a solution of silver salt and the other of a trivalent-metal salt, are connected in series and a current of 2A is maintained for 1.50 hours. It is found that 1.00g of the trivalent-metal is deposited.
- What is the atomic weight of the trivalent metal?
- How much silver is deposited during this period? Atomic weight of silver is 107.9 g/mole.
Answer the following question:
A diver under water, looks obliquely at a fisherman standing on the bank of a lake. Would the fisherman look taller or shorter to the diver than what he actually is?
A diver under water, looks obliquely at a fisherman standing on the bank of a lake. Would the fisherman look taller or shorter to the diver than what he actually is?
When a boron nucleus $\big(\text{ }^{10}_5\text{B}\big)$ is bombarded by a neutron, an $\alpha$-particle is emitted. Which nucleus will be formed as a result?
→What was the difficulty with the wave theory ? How was this difficulty explained using Maxwell's Electro-magnetic wave theory ?
If the sound level in a room is increased from 50dB to 60dB, by what factor is the pressure amplitude increased?
Write any four general properties of electric field lines.
A conducting circular loop having a radius of 5.0cm, is placed perpendicular to a magnetic field of 0.50T. It is removed from the field in 0.50s. Find the average emf produced in the loop during this time.
What does the equivalence / similarity of magnetic field lines of a bar magnet and a solenoid indicate (suggest)?