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∫20x(5x2+x-2) dx
∫4(102x^2) dx
verify green's theorem by the force field F(x,y)= x^2 i - xy j , in moving a particle along the circle with in the first quadrent (x^2 + y-2)^2 = 4
A manufacturer wants to build a spring that takes a force 10 N (in negative direction) to compress it 0.2 m from the equilibrium position. The spring should be able to stretch 0.5 m from the equilibrium position.
As a mechanical engineer, you were asked to present how much work should be done to stretch the spring.The presentation shall include important components of the problem, complete and correct computations and a logical and organized explanation.
Hints:
First, create a force function F(x) by finding the spring constant k in F(x) = kx where F(x) is the force and x is the position from the equilibrium.
Then, calculate work ustng the concept of the definite integral.
If a variable force F(x) moves an object in a positive direction along the x-axis from point a to point b, then the work done on the object is W = ∫ ^b a F(x) dx
A manufacturer wants to build a spring that takes a force 10 N (in negative direction) to compress it 0.2 m from the equilibrium position. The spring should be able to stretch 0.5 m from the equilibrium position.
As a mechanical engineer, you were asked to present how much work should be done to stretch the spring.The presentation shall include important components of the problem, complete and correct computations and a logical and organized explanation.
Hints:
First, create a force function F(x) by finding the spring constant k in F(x) = kx where F(x) is the force and x is the position from the equilibrium.
Then, calculate work ustng the concept of the definite integral.
If a variable force F(x) moves an object in a positive direction along the x-axis from point a to point b, then the work done on the object is W = ∫ ^b a F(x) dx
Check whether the function: f: R^2→R, defined by
f(x,y)= x+ysinx has extremum at any point in the domain of f.
1. Indicate which relationship is direct or partial variation. How do you know?
1b Integrate the following expressions.
∫(3𝑥3−4𝑥2+5𝑥−3)𝑑𝑥
∫(3𝑐𝑜𝑠2𝜃+5𝑐𝑜𝑠4𝜃)𝑑𝜃
The power (in watts) from an engine is represented by the equation: 𝑃=100𝑡1.4+6𝑡 where t is the time in seconds. i. Draw the graph that represents power against time for this engine. ii. Show the area on the graph which represents the energy converted between 5 s and 15 s. iii. Show, using summation, how you would gain an approximation for the energy. iv. Using integration, evaluate the exact energy between 5 s and 15 s.
The acceleration of a moving object can be modelled by the following
equation.
a = 3t^2
i) Using integration v = ∫ a dt to find the value of the velocity value of
the velocity at 0 ≤ t ≤ 2.2 (s).
ii) Using trapezium rules (n=6) to find the mean value of the velocity over
a range of 0 ≤ t ≤ 2.2.
iii) Using a computer spreadsheet to increase the number of intervals to
n=12 for the numerical method and compare your obtained results
with (i) and (ii).
iv) Evaluate all obtained results (form i to iv steps) using technically correct
language and a logical structure to identify whether the size of
numerical steps (intervals) and applied various numerical techniques
have affected the obtained result.
find dy/dx
y = 3cosh √x -3e^2x
