Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Please verify your account before proceeding.

In this lesson, we will learn how to apply the net change theorem.

Q1:

True or False? The Net Change Theorem says that οΈ β π₯ π₯ = β 9 β β 4 9 4 d .

Q2:

True or False: If π ( π‘ ) represents the rate of change of a catβs weight in kilograms per month when it is π‘ months old, then οΈ π ( π‘ ) π‘ 4 0 d equals the catβs weight when it is 4 months old.

Q3:

True or False: The net change theorem states that οΈ π₯ β π‘ π‘ = β π₯ β β π π₯ π d d d .

Q4:

A particleβs velocity in metres per second as a function of time is π£ ( π‘ ) = 2 π‘ β 5 π‘ β 3 2 . What distance does it travel between π‘ = 2 and π‘ = 4 ?

Q5:

A particleβs velocity in metres per second as a function of time is π£ ( π‘ ) = 5 π‘ β 3 . What distance does it travel between π‘ = 0 and π‘ = 1 ?

Q6:

Suppose that πΉ ( π‘ ) = π‘ 2 . Evaluate οΈ πΉ β² ( π‘ ) π‘ 3 1 d using the net change theorem.

Q7:

An oil tanker leaks at the rate π = π ( π‘ ) cubic litres per minute, where π‘ is minutes after the accident. Write an integral that expresses the volume of oil leaked out in the first hour.

Q8:

A particleβs velocity in metres per second as a function of time is π£ ( π‘ ) = 2 π‘ β 3 π‘ β 5 2 . What distance does it travel between π‘ = 1 and π‘ = 4 ?

Q9:

A particleβs velocity in metres per second as a function of time is π£ ( π‘ ) = 2 π‘ β 3 π‘ β 5 2 . What distance does it travel between π‘ = 1 and π‘ = 3 ?

Q10:

A particleβs velocity in metres per second as a function of time is π£ ( π‘ ) = 4 π‘ β 1 . What distance does it travel between π‘ = 0 and π‘ = 2 ?

Q11:

A particleβs velocity in metres per second as a function of time is π£ ( π‘ ) = 2 π‘ β 3 . What distance does it travel between π‘ = 0 and π‘ = 5 ?

Q12:

A particleβs velocity in metres per second as a function of time is π£ ( π‘ ) = 2 π‘ β 3 . What distance does it travel between π‘ = 0 and π‘ = 4 ?

Donβt have an account? Sign Up