Answer:
a) ⅓ units²
b) 4/15 pi units³
c) 2/3 pi units³
Step-by-step explanation:
4y = x²
2y = x
4y = (2y)²
4y = 4y²
4y² - 4y = 0
y(y-1) = 0
y = 0, 1
x = 0, 2
Area
Integrate: x²/4 - x/2
From 0 to 2
(x³/12 - x²/4)
(8/12 - 4/4) - 0
= -⅓
Area = ⅓
Volume:
Squares and then integrate
Integrate: [x²/4]² - [x/2]²
Integrate: x⁴/16 - x²/4
x⁵/80 - x³/12
Limits 0 to 2
(2⁵/80 - 2³/12) - 0
-4/15
Volume = 4/15 pi
About the x-axis
x² = 4y
x² = 4y²
Integrate the difference
Integrate: 4y² - 4y
4y³/3 - 2y²
Limits 0 to 1
(4/3 - 2) - 0
-2/3
Volume = ⅔ pi
Y=5+x is the inaquality you are looking for.
Given:
The function is:
To find:
The steps of finding the inverse function 
.
Solution:
We have,
The steps of finding the inverse function are:
Step 1: Substitute 
.
Step 2: Interchange x and y.
Step 3: Taking square on both sides, we get
Step 4: Adding 21 on both sides, we get
Step 5: Divide both sides by 7.
Step 6: Substitute 
.
, where 
.
Therefore, the inverse of the given function is 
and the arrangement of steps is shown above.
