Question:
Simpson's \( \frac{1}{3} \) rule is applied when
Simpson's \( \frac{1}{3} \) rule is applied when
Show Hint
Ensure the number of intervals is even when using Simpson's \( \frac{1}{3} \) rule to ensure the calculation is accurate.
Updated On: Jun 18, 2025
- the number of intervals is divisible by 3
- the number of intervals is divisible by 2
- the number of intervals is divisible by 5
- the number of intervals is divisible by 7
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Simpson's \( \frac{1}{3} \) rule is a numerical method for approximating definite integrals. For the rule to be applicable, the number of intervals must be even. This is because the formula involves pairing values from consecutive intervals, and for this pairing to be possible, the number of intervals must be divisible by 2.
Therefore, the correct condition is that the number of intervals is divisible by 2.
Was this answer helpful?
0
0
Top Questions on Calculus
- If \( f(3)=18,\; f'(3)=0 \) and \( f''(3)=4 \), then the value of \[ \lim_{x\to 1}\ln\left(\frac{f(x+2)}{f(3)}\right)^{\frac{18}{(x-1)^2}} is: \]
- The value of \[ \int_{\frac{\pi}{6}}^{\pi} \frac{\pi + 4x^{11}}{1 - \sin\left(|x| + \frac{\pi}{6}\right)}\,dx is: \]
If the system of equations \[ x + 2y - 3z = 2, \quad 2x + \lambda y + 5z = 5, \quad 14x + 3y + \mu z = 33 \]
has infinitely many solutions, then \( \lambda + \mu \) is equal to:
- If $y = \sin^{-1} x$, then $(1 - x^2) \frac{d^2y}{dx^2}$ is equal to :
- The derivative of \(\sin\left(\tan^{-1} e^{2x}\right)\) with respect to \(x\) is:
View More Questions
Questions Asked in AP PGECET exam
- The absolute humidity of air at 101.325 kPa is measured to be 0.02 kg of water per kg of dry air. Then the partial pressure of water vapour in the air is:
- AP PGECET - 2025
- Thermodynamics
- If the vapour pressure at two temperatures of a solid phase in equilibrium with its liquid phase is known, then the latent heat of fusion can be calculated by the:
- AP PGECET - 2025
- Thermodynamics
- 1 mole of Argon gas is heated at constant pressure from 200 K to 600 K.
If \( C_p = 4\ \text{cal} \cdot \text{deg}^{-1} \cdot \text{mol}^{-1} \), then the change in entropy will be:
(Given \( \ln 3 = 1.09 \))
- AP PGECET - 2025
- Thermodynamics
- The minimum amount of work required to operate a refrigerator which removes 1000 Cal heat at $0^\circ$C and rejects at $50^\circ$C will be:
- AP PGECET - 2025
- Thermodynamics
- The entropy of single crystalline Silicon at absolute zero will be:
- AP PGECET - 2025
- Thermodynamics
View More Questions