- #1
bobsmith76
- 336
- 0
Homework Statement
The Attempt at a Solution
I dont' see why you don't take the antiderivative of pix^(1/2) which makes it
(2pix^(3/2))/3
Calculating Volume of a Solid Using Integrals
Click For Summary
SUMMARY
The discussion focuses on calculating the volume of a solid using integrals, specifically addressing the antiderivative of the function \(\pi x^{1/2}\). The correct approach involves recognizing that the integrand is \(\pi [\sqrt{x}]^2\), leading to the antiderivative \(\frac{2\pi x^{3/2}}{3}\). This clarification highlights a common misunderstanding in interpreting the integrand, emphasizing the importance of accurate mathematical representation in volume calculations.
PREREQUISITES- Understanding of integral calculus
- Familiarity with antiderivatives
- Knowledge of solid geometry concepts
- Basic proficiency in mathematical notation
- Study the application of definite integrals in volume calculations
- Learn about the method of disks and washers for volume determination
- Explore the concept of triple integrals in three-dimensional space
- Review examples of volume calculations using integrals in calculus textbooks
Students studying calculus, educators teaching integral calculus, and anyone interested in understanding the application of integrals in calculating volumes of solids.
I dont' see why you don't take the antiderivative of pix^(1/2) which makes it
(2pix^(3/2))/3
- #2
jbunniii
Homework Helper
- 3,488
- 257
Because the integrand is [itex]\pi [\sqrt{x}]^2[/itex], not [itex]\pi \sqrt{x}[/itex].
- #3
bobsmith76
- 336
- 0
thanks. my book did a real poor job of explaining that.