- #1
bobsmith76
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Homework Statement
I understand everything except for the part where the -1 pops out of nowhere on step 4. why? how?
Calculating Cone Surface Area | Step-by-Step Guide
- Thread starter bobsmith76
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- Area Cone Surface Surface area
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SUMMARY
The discussion focuses on calculating the surface area of a cone using integral calculus. The key point addressed is the confusion surrounding the appearance of the -1 in step 4 of the calculation. The integral is defined as \(\int^{b}_{a}f(x)dx\), which simplifies to \(F(b) - F(a)\). The -1 arises from substituting the lower limit (x = 0) into the integral, which is then subtracted from the upper limit (x = 1/2).
PREREQUISITES- Understanding of integral calculus
- Familiarity with the Fundamental Theorem of Calculus
- Knowledge of function notation and limits
- Basic skills in evaluating definite integrals
- Study the Fundamental Theorem of Calculus in detail
- Practice evaluating definite integrals with varying limits
- Explore applications of integral calculus in geometry, specifically cone surface area
- Learn about common pitfalls in integral calculations and how to avoid them
Students studying calculus, educators teaching integral calculus, and anyone looking to deepen their understanding of geometric applications of integrals.
I understand everything except for the part where the -1 pops out of nowhere on step 4. why? how?
- #2
Mentallic
Homework Helper
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Remember that when you solve an integral, you need to take the integral of the highest value minus lowest value. So if you want to solve
\int^{b}_{a}f(x)dx
Then you'll have
=\left[F(x)\right]^b_a
=F(b)-F(a)
\int^{b}_{a}f(x)dx
Then you'll have
=\left[F(x)\right]^b_a
=F(b)-F(a)
- #3
wukunlin
Gold Member
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the 1 is the result of substituting the lower limit of the previous step, ie x = 0, which subtracted from the upper limite of the previous step, x = 1/2
edit: oops. too late
edit: oops. too late
- #4
bobsmith76
- 336
- 0
thanks, I got it.
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