Unit 4 Calculator Section

Front

What is the formula for finding the area between a curve and the x-axis?

Back

The area A between a curve f(x) and the x-axis from x=a to x=b is given by A = ∫[a,b] f(x) dx.

Front

How do you determine the area between two curves f(x) and g(x)?

Back

The area A between two curves f(x) and g(x) from x=a to x=b is given by A = ∫[a,b] (f(x) - g(x)) dx, where f(x) is the upper curve and g(x) is the lower curve.

Front

What is the significance of the definite integral in calculating area?

Back

The definite integral calculates the net area under a curve, accounting for areas above the x-axis as positive and below as negative.

Front

How do you find the points of intersection between two curves?

Back

To find the points of intersection between two curves f(x) and g(x), set f(x) = g(x) and solve for x.

Front

What is the displacement of a particle in motion?

Back

Displacement is the net change in position of a particle, calculated as the definite integral of the velocity function over a given interval.

Front

What is the difference between displacement and distance traveled?

Back

Displacement is the net change in position, while distance traveled is the total length of the path taken, regardless of direction.

Front

Back

Front

Back

Front

What is the velocity function and how is it used in motion problems?

Back

The velocity function v(t) describes the rate of change of position with respect to time. It is used to find displacement and distance traveled by integrating over a time interval.

Front

How do you find the total distance traveled by a particle given its velocity function?

Back

To find the total distance traveled, calculate the integral of the absolute value of the velocity function over the given interval.