## The area of the curvilinear trapezoid

The area of the curvilinear trapezoid bounded by the graph of the positive continuous on a segment functions, axis and straight and equal

**Example.**To calculate the area of the figure bounded by the lines

Portraying these lines produced curvilinear trapezoid

## The area of the figure bounded the graphs of two functions and the direct and

If on a given interval of continuous function and have the property that for all then

**Example.**To calculate the area of the figure bounded by the lines

Draw the specified line and the abscissa of their intersection points.

The abscissa of the intersection points:

Then according to the formula

## The volume of the bodies

### In the General case

If the body is encased between two perpendicular to the axis planes passing through the points and then

where is the cross-sectional area of the body a plane that passes through the point and perpendicular to the axis

### For the body rotation

If the body obtained by rotation around the axis of a curvilinear trapezoid, limited by schedule and newme continuous functions on the interval and straight and then