Respuesta :
The total distance traveled by the particle from t=0 to t=1.5 is 0.496 units.
What is integration?
It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.
The total distance traveled by the particle can be given by:
[tex]\rm d = \int\limits^2_0 {x'(t)} \, dt \ + \int\limits^4_0 {y'(t)} \, dt \\[/tex] .....(1)
First solving for:
[tex]=\rm \int\limits^2_0 {x'(t)} \, dt \[/tex]
Where x'(t) =(t−1)e^t^ 2
After evaluating the definite integral, we get:
[tex]\rm \int\limits^2_0 {x'(t)} \, dt \ = 0.18075[/tex]
For:
[tex]\rm = \int\limits^4_0 {y'(t)} \, dt \\[/tex]
Where y′(t) = sin(3−3t^2)
The value of the above definite integration is:
[tex]\rm = \int\limits^4_0 {y'(t)} \, dt = 0.3149[/tex]
Now substituting in the equation (1), we get:
= 0.18075 + 0.3149
= 0.4956 ≈ 0.496 units.
Thus, the total distance traveled by the particle from t=0 to t=1.5 is 0.496 units.
Learn more about integration here:
https://brainly.in/question/4630073
