Simplify the integrands by polynomial division.
Now computing the integrals is trivial.
5.
where we use the power rule,
and a substitution to integrate the last term,
8.
using the same approach as above.
Rotation means rotating a shape through certain angle.
The shape can be one Dimensional , 2 dimensional or 3 Dimensional.
Angle of rotation lies between 0 degrees to 360 degrees.
The point (x,y) lies in two Dimensional coordinate system.
Since point (x,y) is rotated and we are getting new coordinate as (y,-x).
The point (x,y) lies in first quadrant and the point (y,-x) lies in fourth quadrant.
Also,Distance of x-coordinate from X-axis=Distance of y coordinate from Y-axis
,Distance of y-coordinate from Y-axis=Distance of x coordinate from X-axis
So, Either the shape is rotated through anticlockwise motion through an angle of 270 degrees or through an angle of 90 degrees in clockwise motion.
The unit vector is given by the following formula:
a '= (a) / (lal)
Where,
a: vector a
lal: Vector module a
We are looking for the module:
lal = root ((- 15) ^ 2 + (8) ^ 2)
lal = 17
Same direction:
a = -15i + 8j
The unit vector is:
a '= (1/17) * (- 15i + 8j)
Opposite direction:
a = 15i - 8j
The unit vector is:
a '= (1/17) * (15i - 8j)
Answer:
a unit vector that has the same direction as the vector a is:
a '= (1/17) * (- 15i + 8j)
a unit vector that has the opposite direction of the vector a is:
a '= (1/17) * (15i - 8j)
F(6) = 7(6) - 4
f(6) = 42 - 4
f(6) = 38
Hope this helps!