CALCULUS HELP! Find the volume of the solid obtained by rotating the region under the graph of the function
1 answer:
Answer:
14π
Step-by-step explanation:
Graph the region. Rotated about the y-axis, the volume is a round, spherical shape.
Slice the volume into a vertical stack of discs. The radius of each disc is x, the thickness of each disc is dy. The volume of each disc is:
dV = π x² dy
dV = π (7 sin y) dy
dV = 7π sin y dy
The total volume is the sum of all the discs from y=0 to y=π.
V = ∫ dV
V = ∫₀ᵖⁱ 7π sin y dy
V = -7π cos y |₀ᵖⁱ
V = -7π (cos π − cos 0)
V = -7π (-1 − 1)
V = 14π
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Answer:
x = 8 units.
Step-by-step explanation:
I think your question is missed of key information, allow me to add in and hope it will fit the original one.
<em>The areas of the squares adjacent to two sides of a right triangle are 32 unit square and 32 units square. Find the length,x, of the third side of the triangle</em>
My answer:
- Let a is the side length of the 1st square
The area of the 1st square is equal to 32 units square
<=>
<=> a = units
- Let b is the length of the 2nd square
The area of the 2nd square is equal to 32 units square
<=> = 32
<=> b = units
- Find the value of x
Applying the Pythagoras Theorem, we have:
<=>
<=>
<=> x = 8 units
Hope it will find you well.