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
