Antiderivatives and rules of integration Antiderivatives and rules - - PowerPoint PPT Presentation

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Aug 21, 2022 212 likes •397 views

Antiderivatives and rules of integration Antiderivatives and rules of integration Problem Antiderivatives and rules of integration Problem A fighter aircraft is launched from a deck of an aircraft carrier with the help of a steam catapult.

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Antiderivatives and rules of integration

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Problem

Antiderivatives and rules of integration

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Problem

A fighter aircraft is launched from a deck of an aircraft carrier with the help of a steam catapult.

Antiderivatives and rules of integration

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Problem

A fighter aircraft is launched from a deck of an aircraft carrier with the help of a steam catapult.

◮ Assume that the aircraft is initially at rest

Antiderivatives and rules of integration

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Problem

A fighter aircraft is launched from a deck of an aircraft carrier with the help of a steam catapult.

◮ Assume that the aircraft is initially at rest ◮ If the aircraft is to attain a takeoff speed of at least

240 ft/sec after traveling 800 ft along the flight deck find

Antiderivatives and rules of integration

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Problem

A fighter aircraft is launched from a deck of an aircraft carrier with the help of a steam catapult.

◮ Assume that the aircraft is initially at rest ◮ If the aircraft is to attain a takeoff speed of at least

240 ft/sec after traveling 800 ft along the flight deck find

◮ the minimum acceleration to which it must be subjected,

assuming that it is constant.

Antiderivatives and rules of integration

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Problem

Antiderivatives and rules of integration

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Problem

The rate of change of the velocity of blood r cm from the central axis of an artery is given by

Antiderivatives and rules of integration

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Problem

The rate of change of the velocity of blood r cm from the central axis of an artery is given by a(r) = −vr

Antiderivatives and rules of integration

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Problem

The rate of change of the velocity of blood r cm from the central axis of an artery is given by a(r) = −vr where k is constant.

Antiderivatives and rules of integration

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Problem

The rate of change of the velocity of blood r cm from the central axis of an artery is given by a(r) = −vr where k is constant.

◮ If the radius of an artery is R, find an expression for the

velocity of blood as a function r

Antiderivatives and rules of integration

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Problem

The rate of change of the velocity of blood r cm from the central axis of an artery is given by a(r) = −vr where k is constant.

◮ If the radius of an artery is R, find an expression for the

velocity of blood as a function r assuming that the velocity

f blood on the wall of the artery is zero

Antiderivatives and rules of integration

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Problem

Antiderivatives and rules of integration

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Problem

During a thunderstorm, rain was falling at a rate of

Antiderivatives and rules of integration

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Problem

During a thunderstorm, rain was falling at a rate of 8 √ 2t − 32t3 0 ≤ t in/hr

Antiderivatives and rules of integration

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Problem

During a thunderstorm, rain was falling at a rate of 8 √ 2t − 32t3 0 ≤ t in/hr

◮ Find an expression giving the total amount of rainfall after

t hours

Antiderivatives and rules of integration

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Problem

During a thunderstorm, rain was falling at a rate of 8 √ 2t − 32t3 0 ≤ t in/hr

◮ Find an expression giving the total amount of rainfall after

t hours

◮ How much rain had fallen after 1/2 hr.

Antiderivatives and rules of integration