Continuous Functions and Integration: True or False?

Thread starter dnt
Start date Aug 7, 2006
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Couple

In summary, a "Couple T/F calc question" is a scientific problem that involves calculating the torque of a couple acting on an object. To solve these questions, you need to use the equation τ = r x F and pay attention to the direction of the forces and use the right-hand rule. Common misconceptions about these questions include the belief that the magnitude of the torque is equal to the sum of the individual forces and that the direction of the torque is always the same as the direction of the forces. To check your answer, you can use the right-hand rule and plug your values into the equation. Some real-world applications of "Couple T/F calc questions" include analyzing the rotational forces in engineering, physics, and biomechan

Aug 7, 2006

dnt

a) if f and g are continuous on [a,b] then:

int [f(x)g(x) dx] = int [f(x) dx] * int [g(x) dx]

i said false.

b) if f is continuous on [a,b] then

int [xf(x) dx] = x int [f(x) dx]

again i said false (x isn't constant)

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Aug 7, 2006

d_leet

Yep. you're right in both cases.

1. What is a "Couple T/F calc question"?

A "Couple T/F calc question" is a type of scientific problem that involves calculating the torque, or rotational force, of a couple (two equal and opposite forces) acting on an object. These questions typically involve determining the direction and magnitude of the torque in a given scenario.

2. How do I solve a "Couple T/F calc question"?

To solve a "Couple T/F calc question", you will need to use the equation τ = r x F, where τ is the torque, r is the distance from the pivot point to the point where the force is applied, and F is the magnitude of the force. Make sure to pay attention to the direction of the forces and use the right-hand rule to determine the direction of the torque.

3. What are some common misconceptions about "Couple T/F calc questions"?

One common misconception is that the magnitude of the torque is equal to the sum of the individual forces. In reality, the magnitude of the torque is equal to the product of the individual forces and the distance between them. Another misconception is that the direction of the torque is always the same as the direction of the forces. The direction of the torque depends on the direction of the forces and the distance between them.

4. How can I check my answer for a "Couple T/F calc question"?

To check your answer, you can use the right-hand rule to determine the direction of the torque and then plug your values into the equation τ = r x F. Make sure to use the correct units and pay attention to the direction of the torque. You can also compare your answer to the expected answer or ask a fellow scientist to check your work.

5. What are some real-world applications of "Couple T/F calc questions"?

Couple T/F calc questions are commonly used in engineering and physics to analyze the rotational forces acting on objects, such as bridges, buildings, and machinery. They are also used in biomechanics to study the forces and torques involved in human movement. Understanding how to solve these types of questions is essential for designing and analyzing structures and machines in the real world.