Answer:
Option B
Step-by-step explanation:
First term of the given arithmetic sequence 'a' = -3
Common difference in each successive term 'd' = -8 - (-3)
d = -5
Explicit formula for an arithmetic sequence will be,
Here, n = number of term
= nth term of the sequence
For n = 23,
= -3 + (23 - 1)(-5)
= -3 - 110
= -113
Option B is the answer.
Answer:
∫₋₃¹ π y⁴ dy
Step-by-step explanation:
If we slice the solid shape, we get circular cross sections or disks. The thickness of each disk is dy. The radius of each disk is x. So the volume of each disk is:
dV = π r² h
dV = π x² dy
Since x = y²:
dV = π y⁴ dy
The total volume is the sum of all the disks from y=-3 to y=1.
V = ∫ dV
V = ∫₋₃¹ π y⁴ dy
