Answer:
Indefinite integration acts as a tool to solve many physical problems.
There are many type of problems that require an indefinite integral to solve.
Basically indefinite integration is required when we deal with quantities that vary spatially or temporally.
As an example consider the following example:
Suppose that we need to calculate the total force on a object placed in a non- uniform field.
As an example let us consider a rod of length L that posses an charge 'q' per meter length and suppose that we place it in a non uniform electric field which is given by
Now in order to find the total force on the rod we cannot use the similar procedure as we can see that the force on the rod varies with the position of the rod.
But if w consider an element 'dx' of the rod at a distance 'x' from the origin the force on this element will be given by
Now to find the whole force on the rod we need to sum this quantity over the whole length of the rod requiring integration, as shown
Similarly there are numerous problems considering motion of particles that require applications of indefinite integration.
Step-by-step explanation:
cos θ = 3 / AB
When θ = 28°:
cos 28° = 3 / AB
AB = 3 / cos 28°
AB ≈ 3.4
When AB = 5.2:
cos θ = 3 / 5.2
θ = cos⁻¹(3 / 5.2)
θ ≈ 54.8°
Answer:
x = 1
Step-by-step explanation:
8 -(x+5) = 5x - 3
-(x+5) ---> -1 (x +5) = -x - 5
8 - x - 5 = 5x -3 8 - 5 = 3
-x + 3 = 5x - 3
+x +x
3 = 6x - 3
+3 +3
6 = 6x
/6 /6
<u>x = 1</u>
Answer:
Total possible number of outcomes = C(24,6) [24 choose 6]
=24!/(6!18!)
= 134596
Out of which there is only one winning combination.
Therefore we conclude:
P(win 20000)=1/134596
P(lose 1)=134595/134596
and hence the expected value is:
20000*(1/134596)+(-1)*(134595/134596)
=-114595/134596
=-0.8514 (rounded to four places after decimal)
Step-by-step explanation:
Hope this helped!
Complete question:
y = 2x² + 2x - 3
x = -2 -1 0 1 2
Answer:
<u>Complete table of values</u>
x: -2 -1 0 1 2
y: 1 -3 -3 1 9
Step-by-step explanation:
Given;
y = 2x² + 2x - 3
To complete the table of values of the equation above, we substitute the value of x into the given equation and solve for y.
when, x = -2
y = 2(-2)² + 2(-2) - 3
y = 8 - 4 - 3
y = 1
when x = -1
y = 2(-1)² + 2(-1) - 3
y = 2 - 2 - 3
y = -3
when x = 0
y = 2(0)² + 2(0) - 3
y = 0 - 0 - 3
y = -3
when x = 1
y = 2(1)² + 2(1) - 3
y = 2 + 2 - 3
y = 1
when x = 2
y = 2(2)² + 2(2) - 3
y = 8 + 4 - 3
y = 9
<u>Complete table</u>
x: -2 -1 0 1 2
y: 1 -3 -3 1 9
