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:
the answer is in the image
Here we can simplify the product by multiply the square root 2 with square root 2 first.
=3*2
=6
So answer is 6
Given :
A boat is located a sea level. A scuba diver is 80 feet along the surface of the water from the boat and 30 feet below the water surface.
A fish is 20 feet along the horizontal plane from the scuba diver and 10 feet below the scuba diver.
To Find :
The slope between the scuba diver and fish.
Solution :
Horizontal distance between diver and fish is 20 feet.
Fish is 10 feet below the scuba diver.
Slope between scuba diver and fish is :
Therefore, the slope between the scuba diver and fish is 0.5 .
First you open 2 parenthesis with x in each one:
(x )(x )=0
Then, you place the sign of the second term (the x term) in the first parenthesis.
(x+ )(x )=0
Next, you multiply the signs of the x term and the sign of the constant (the third term).
Since + × - = -, then you place a -.
(x+ )(x- )=0
You look at the constant (-18) and the second term (3). What two numbers multiplied give you -18 but subtracted (since the signs inside the parenthesis are opposite) give you 3? Those numbers are 6 and 3.
Since the result of the substraction need to be 3, you place the 6 with the + sign and the 3 with the negative sign (if you think of it, 6-3=3 but 3-6 = -3. That's the reason behind placing the numbers)
(x+6)(x-3)=0
Therefore,
x+6=0 or x-3=0
x=-6 or x=3
Your roots are -6 and 3.
