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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. 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. ◮ Assume that the aircraft is initially at rest 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. ◮ 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

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

Problem Antiderivatives and rules of integration

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

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

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

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

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 of blood on the wall of the artery is zero Antiderivatives and rules of integration

Problem Antiderivatives and rules of integration

Problem During a thunderstorm, rain was falling at a rate of Antiderivatives and rules of integration

Problem During a thunderstorm, rain was falling at a rate of √ 2 t − 32 t 3 0 ≤ t in / hr 8 Antiderivatives and rules of integration

Problem During a thunderstorm, rain was falling at a rate of √ 2 t − 32 t 3 0 ≤ t in / hr 8 ◮ Find an expression giving the total amount of rainfall after t hours Antiderivatives and rules of integration

Problem During a thunderstorm, rain was falling at a rate of √ 2 t − 32 t 3 0 ≤ t in / hr 8 ◮ 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