Calculus 2 Integrals Homework Solutions

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SUMMARY

This discussion focuses on solving specific calculus problems from a homework assignment, particularly problems 1 and 4(a). The second fundamental theorem of calculus is referenced as a key concept. For problem 1, the user attempted to calculate areas under the curve using Riemann sums to approximate f(x) = -0.75. In problem 4(a), the user incorrectly interpreted the integral's limits, leading to confusion regarding the evaluation of f(2) = 3.

PREREQUISITES
  • Understanding of the second fundamental theorem of calculus
  • Familiarity with Riemann sums for area approximation
  • Knowledge of integral and derivative relationships
  • Ability to interpret function evaluations and limits
NEXT STEPS
  • Review the second fundamental theorem of calculus in detail
  • Practice calculating areas under curves using Riemann sums
  • Study the relationship between integrals and derivatives
  • Explore function evaluation techniques and limit concepts
USEFUL FOR

Students studying calculus, particularly those tackling integrals and their applications, as well as educators seeking to clarify common misconceptions in calculus problem-solving.

Kingnabeel
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Homework Statement


Here are the problems
http://imgur.com/a/kbtPS
The problems I need help with are 1 and
4(a)

Homework Equations


The second fundamental theorem of calculus

The Attempt at a Solution


For problem 1, I calculated the areas under the curve (using remmien summs) and tried to find the x value that would approximate f(x)=-.75

For problem 4(a), all i did was that since it was an integral, taking the derivative would just be the integrals and that's how I got that answer.[/B]
 
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I mean integrand
 
For 4(a), the problem with yours is that they are asking for f(2)=3, that is, when x=2 f(x)=3. What you've done is set your interval from x to 2. That means the interval for f(2) is from 2 to 2. Which will always be 0.

I can't tell what is going on for 1. You'll need to explain the question better.
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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