Tongji University Advanced Mathematics Volume 1 Chapter 6 The Application of Definite Integral and a Daily Question

(It’s a bit long to play during the New Year)

Chapter Six: Application of Definite Integral

Knowledge logic structure diagram

Postgraduate exam content

Definite integral expression and calculation of the area of ​​the plane figure, the arc length of the plane curve, the volume and side area of ​​the rotating body, and the area of ​​the parallel section are the average value of the known solid volume, work, gravitation, pressure and functions.

Postgraduate exam requirements

• 1. Master the use of definite integral to express and calculate the area of ​​a plane figure.
• 2. Master the use of definite integral to express and calculate the arc length of a plane curve.
• 3. Master the use of definite integral to express and calculate the volume and side area of ​​a rotating body.
• 4. Master the use of definite integrals to express and calculate the parallel cross-sectional area as the volume of a known solid.
• 5. Understand the expression and calculation of work, gravity, and pressure with definite integrals.
• 6. Know the average value of the function.

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