PRACTICAL CLASS № 9-10
Properties of definite integrals. The Newton-Leibniz formula. Applications of definite integrals in economics. 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: First order differential equations. Differential equations of higher orders.
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).
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | Поиск по сайту:
|