Integration of simple rational fractions. Integration of rational fractions. Integration of expressions containing trigonometric functions. Integration of irrational functions
Theoretical questions:
1. Integration of rational fractions. 2. Integration of expressions containing trigonometric functions. 3. Integration of irrational functions.
Classroom assignments:
1. Calculate integrals:
1. 2. 3.
4. 5.
2. Find integrals using appropriate substitution:
1. 2. 3. 4.
5.
3. Calculate integrals:
1. 2. 3.
4. 5. 6.
7. 8.
Homework:
Theoretical material: The definite integral. Problems leading to the definite integral. The NewtonLeibniz formula.
Solve problems:
Calculate integrals: 1. 2.
3. 4. 5. 6.
7. 8. 9.
10.
PRACTICAL CLASS ¹ 1215
The definite integral. Problems leading to the definite integral. The NewtonLeibniz 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. 2. 3. 4.
5.
2. Calculate integrals: 1. 2. 3. 4. 5.
3. Find the area bounded by the curve , the xaxis, and the lines and .
4. Find the area of the ellipse .
5. Find the area bounded by the curve , for .
6. Find the area of the lemniscate .
7. Find the length of the cissoid from to .
Homework:
Theoretical material: Functions of several variables and main properties. Partial derivatives and differentials.
Solve problems:
1. Find the area bounded by the parabola and the straight line .
2 Find the area bounded by the ellipse .
3. Find the area of the ellipse whose parametric equations are and .
4. Find the parabola from (0,0) to (4,4).
Date: 20150102; view: 1173
