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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 Newton-Leibniz formula.

Solve problems:

Calculate integrals: 1. 2.

3. 4. 5. 6.

7. 8. 9.

 

10.

 

PRACTICAL CLASS 12-15

The 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. 2. 3. 4.

5.

2. Calculate integrals: 1. 2. 3. 4. 5.

3. Find the area bounded by the curve , the x-axis, 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: 2015-01-02; view: 1173


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