Question:
Given $e = 2.72, e^2 =7.39 ,e^3 = 20.09 , e^4 = 54.60 $ the approximate value of $\int\limits_{0}^{4} e^x dx$ using Simpson?? rule and taking $h=1$ is
Given $e = 2.72, e^2 =7.39 ,e^3 = 20.09 , e^4 = 54.60 $ the approximate value of $\int\limits_{0}^{4} e^x dx$ using Simpson?? rule and taking $h=1$ is
Updated On: Jul 6, 2022
- 57.325
- 53.873
- 58.325
- 57.323
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The Correct Option is B
Solution and Explanation
$\int\limits_{0}^{4} f(x) \, dx \cong \frac{h}{3} [ (y_0 + y_4) +4 ( y_1 + y_3 ) + 2y_2 ] , h = 1 $ .
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Concepts Used:
Applications of Integrals
There are distinct applications of integrals, out of which some are as follows:
In Maths
Integrals are used to find:
- The center of mass (centroid) of an area having curved sides
- The area between two curves and the area under a curve
- The curve's average value
In Physics
Integrals are used to find:
- Centre of gravity
- Mass and momentum of inertia of vehicles, satellites, and a tower
- The center of mass
- The velocity and the trajectory of a satellite at the time of placing it in orbit
- Thrust