PRACTICAL CLASS № 12-15The definite integral. Problems leading to the definite integral. The Newton-Leibniz FORMULA. Applications to the computation of the integrals of plane figures areas. Calculation the arc length, the amount of body rotation. The improper integral
Theoretical questions: 1. Newton – Leibniz formula. 2. Basic methods of integration. 3. Geometric applications of the definite integral. Classroom assignments: 1. Find integrals using Newton – Leibniz formula 1. 5. 2. Calculate integrals: 1. 3. Find the area bounded by the curve 4. Find the area of the ellipse 5. Find the area bounded by the curve 6. Find the area of the lemniscate 7. Find the length of the cissoid
Homework: Theoretical material: Functions of several variables and main properties. Partial derivatives and differentials. Solve problems: 1. Find the area bounded by the parabola 2 Find the area bounded by the ellipse 3. Find the area of the ellipse whose parametric equations are 4. Find the parabola
|
2. 
3. 
4. 
2. 
3. 
4. 
5. 
, the x-axis, and the lines 
and 
.
.
, 
for 
.
.
from 
to 
.
and the straight line 
.
.
and 
.
from (0,0) to (-4,4).
