Answer:
½ sec²(x) + ln(|cos(x)|) + C
Step-by-step explanation:
∫ tan³(x) dx
∫ tan²(x) tan(x) dx
∫ (sec²(x) − 1) tan(x) dx
∫ (sec²(x) tan(x) − tan(x)) dx
∫ sec²(x) tan(x) dx − ∫ tan(x) dx
For the first integral, if u = sec(x), then du = sec(x) tan(x) dx.
∫ u du = ½ u² + C
Substituting back:
½ sec²(x) + C
For the second integral, tan(x) = sin(x) / cos(x). If u = cos(x), then du = -sin(x) dx.
∫ -du / u = -ln(u) + C
Substituting back:
-ln(|cos(x)|) + C
Therefore, the total integral is:
½ sec²(x) + ln(|cos(x)|) + C
Answer:
Given speed of trolley = 125 meters per minute
Now we know that
Distance= Speed x time
Thus for the first case since the time of travel is less than 450 seconds thus the distance traveled is less than
Distance < 2.083 x 450 =937.5 meters
hence depending on the given information we cannot come to any conclusion weather the distance travelled is less than 800 m or greater than 800 m.
For the second case
since the time of travel is greater than 400 seconds
Thus the distance traveled is
which is greater than 800 meters.
Answer:
A: 1 < y < 4
Step-by-step explanation:
Hopefully this helps!
It’s a left side 8’5 right????
<span>Simplifying
2x + 5 + 6x + -1 = 120
Reorder the terms:
5 + -1 + 2x + 6x = 120
Combine like terms: 5 + -1 = 4
4 + 2x + 6x = 120
Combine like terms: 2x + 6x = 8x
4 + 8x = 120
Solving
4 + 8x = 120
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-4' to each side of the equation.
4 + -4 + 8x = 120 + -4
Combine like terms: 4 + -4 = 0
0 + 8x = 120 + -4
8x = 120 + -4
Combine like terms: 120 + -4 = 116
8x = 116
Divide each side by '8'.
x = 14.5
Simplifying
x = 14.5</span>
