Simplify the integrand:

Now integrate one term at a time.



Putting everything together,

Answer:
The answer is
.
Step-by-step explanation:
Given:

Multiply by 14 on both the side, it gives
.
Now we add 3 on both sides.

Therefore, the answer is
.
Answer:3 units/s
Step-by-step explanation:
Given

Point P lie on this curve so any general point on curve can be written as 
and 
Distance between Point P and (2,0)

P at x=3 P=2
rate at which distance is changing is



Answer:
0.75 mg
Step-by-step explanation:
From the question given above the following data were obtained:
Original amount (N₀) = 1.5 mg
Half-life (t₁/₂) = 6 years
Time (t) = 6 years
Amount remaining (N) =.?
Next, we shall determine the number of half-lives that has elapse. This can be obtained as follow:
Half-life (t₁/₂) = 6 years
Time (t) = 6 years
Number of half-lives (n) =?
n = t / t₁/₂
n = 6/6
n = 1
Finally, we shall determine the amount of the sample remaining after 6 years (i.e 1 half-life) as follow:
Original amount (N₀) = 1.5 mg
Half-life (t₁/₂) = 6 years
Number of half-lives (n) = 1
Amount remaining (N) =.?
N = 1/2ⁿ × N₀
N = 1/2¹ × 1.5
N = 1/2 × 1.5
N = 0.5 × 1.5
N = 0.75 mg
Thus, 0.75 mg of the sample is remaining.