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Before performing any calculation it's good to recall a few properties of integrals:


So we apply the first property in the first expression given by the question:
![\small \sf{\longrightarrow\int ^3_{-2} [2f(x) +2]dx= 2 \int ^3 _{-2} f(x) dx+ \int f^3 _{2} 2dx=18}](https://tex.z-dn.net/?f=%5Csmall%20%5Csf%7B%5Clongrightarrow%5Cint%20%5E3_%7B-2%7D%20%5B2f%28x%29%20%2B2%5Ddx%3D%202%20%5Cint%20%5E3%20_%7B-2%7D%20f%28x%29%20dx%2B%20%5Cint%20f%5E3%20_%7B2%7D%202dx%3D18%7D)
And we solve the second integral:


Then we take the last equation and we subtract 10 from both sides:


And we divide both sides by 2:


Then we apply the second property to this integral:

Then we use the other equality in the question and we get:


We substract 8 from both sides:

• 
Answer:
x=1
Step-by-step explanation:
hope this helps!
Find an explicit formula for the sequence 30\,,\,150\,,\,750\,,\,3750,...30,150,750,3750,...30, space, comma, space, 150, space,
OverLord2011 [107]
The series shown is an geometric series and the explicit formula is given by:
an=ar^(n-1)
where
a=first term
n=number of terms
r=common ratio
from the sequence:
a=30
r=5
thus the explicit formula will be:
an=30(5)^(n-1)
hence the answer is:
an=30(5)^(n-1)
Step-by-step explanation:
s1 = 300
s2 = s1 × 2 = 300 × 2 = 600
s3 = s2 × 2 = s1 × 2² = 1200
sn = sn-1 × 2 = s1 × 2^(n-1)
s7 = 300 × 2⁶ = 300 × 64 = 19,200