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by writing it as a sum of definite integrals.
.
.
and the abscissa axis on the interval 
.
is given:
. Draw a graph of the linear function 
.
which intersects the x-axis at an angle 
.
?
, when limited by the interval 
on the x-axis?
on the interval 
, estimate the definite integral 
.
.
is given:
.
and 
, and the graph of the function 
.
is given.
and 
such that 
is a double zero of the polynomial 
.
. Draw a graph of the polynomial.
, and the coordinate axes.
is given.
with the x-axis.
at the point 
with the x-axis.
is given.
and determine the range and domain of the function.
is increasing.
?
is given:
is given.
.
is given.
function.
.
and the abscissa axis.
and the abscissa axis.
and the abscissa axis.
and the abscissa axis.
and the abscissa axis.
into two decimal places such that the area of the figure bounded by the graph of the function 
and the abscissa axis will be equal to 
.
and 
.
and 
are given.
and 
in the same coordinate system.
and the abscissa on the interval 
.
and the line 
are given.
function around the abscissa axis by 
.
function, the line 
, and the x-axis.
is given.
such that the polynomial 
will have a zero at 
, and find the remaining zeros of the polynomial.
, radius 
, elastic modulus 
and cross section 
, with a force of 
through a distance of 
?
such that the area of the shaded region between the graph of the function 
, the line 
and the abscissa is equal to 1.
such that the area between the graph of the function 
, the abscissa axis, and the lines 
and 
is equal to 
.
, write the function rule, zeros, maximum and draw a parabola that is a graph of the function 
.
calculate the area of the region between the parabola and the chord that connects the threads and the right intersection of the parabola with the 
axis.
and the function 
.
tangent to the graph of the function 
function. The area of the figure is 
. Calculate the value of a using definite integral.
.
we place the tangent to the parabola. Write down the equation of the tangent.
and the abscissa axis forms a simple figure. Calculate its area.
and 
rotates around side 
. Calculate the area and volume of the body formed.
, 
and 
rotates around side 
. Calculate the area of the resulting spindle.
at interval 
around the abscissa axis. Calculate the volume of the resulting spindle.
and 
, with limits: 
and 
is given.
and 
.
and 
. Calculate the area of the figure between the graphs of the f and g functions between the intersections.
and 
.
is given.
function at point 
with the abscissa 
.
and the abscissa. Calculate the exact value of the shaded area.
and 
. The area bounded by the graph of the f function and the abscissa on the interval 
is 
. The area bounded by the graph of the f function and the abscissa axis on the interval 
is 
(see figure below).
. The 
function is specified with 
.
function, which passes through the point 
, and its derivative 
.
and 
are given.
, for which the area of the figure bounded by the graphs of the functions f and g, the abscissa, and line with the equation 
, is equal to 
.
. A graph of the function 
is drawn in the coordinate system, which is parallel to the function f. Write down the function regulation for the function 
in the coordinate system.
function with limit 
, is mirrored over the bisector of the odd quadrants 
. Thus we obtained a graph of the 
function.
.
and 
and 
are given as: 
and 
. Calculate the area of the region bounded by the graphs of 
is given.
and 
.
intersects the asymptote with the equation 
of the given hyperbola at point P. Let 
and 
be the foci of the given hyperbola. Calculate the points 
and 
. Calculate the volume of the solid of revolution V.
and
.
.
, where 
.
let 
denote the area of the figure bounded by the graph of the function f by the abscissa axis between two adjacent zeros 
and 
Prove that for each 
the area is 
.
is given with the regulation 
.
. Calculate all zeros of the f function.
we place the tangent to the graph of the f function. Calculate its equation.
which is considered to be 
and 
.
and 
. In the table below, indicate whether the value in the first column is positive or negative or equal to 0. (See the solved example in the first row).
is given.
.
.
and 
is equal to 
.
. The speed of the aircraft in 
is described by the function 
. How far did the aircraft travel in 120 seconds?
axis and the function 
. Calculate the volume of the solid of revolution that is obtained on the interval 
when we rotate the figure 
around the 
and 
. Determine the volume of the solid of revolution that is obtained when we rotate the figure around the 
axis 
.
and the lines 
.
, and the lines 
and 
.
on the interval 
and the ordinate axis for 
around the ordinate axis.
and 
functions. The figure is rotated around the 
axis.
is given, where 
. Calculate the parameter 
if the area of the figure between the graph of the function 
and the axis 
on the interval 
is equal to 
.
such that the area of the figure under the parabola 
and the abscissa axis on the interval 
is equal to 
.
is given.
function.
function and the line 
at the intersection with the positive abscissa.
away from the horizontal asymptote of this function.
and 
in a given coordinate system. Calculate the area of the figure bounded by the graphs of both functions.
function. Calculate the area of the shaded figure.
is given.
. Write down the domain and range of the 
function and calculate it's zero.
we place the normal on the curve 
. Write the equation of this normal.
, where 
. Determine a such that the area of the figure between the graph of the h function and the x axis on the interval 
is equal to 
.
, where 
. Define b such that the area of the figure between the graph of the u function and the y axis is equal to 
.
, be the point on the graph of the polynomial 
and 
be the perpendicular projection of the point 
on the abscissa. Calculate the abscissa of the point 
is greatest. 
is the origin of the coordinate system.
. The area of the shaded figure is 
. Calculate the value of the parameter a.
and 
are given.
and 
.
and 
. Draw a graph of both functions in a given coordinate system.
.
such that the area of the figure enclosed by the graph of the function 
with the axis 
on the interval 
is equal to 
.
function. Calculate the value of 
to two decimal places if the area of the shaded figure in the graph is equal to 4.
, Calculate:
that applies to the equation:
does the graph of the function 
touch the 
axis? For which number 
is parallel to the line 
.
is the zero of the 
such that the area of the figure between the graph of the 
is equal to 
.
rule is given.
function in the coordinate system. Prove that the tangents to the graph of the function 
axis are perpendicular to each other.
is an ellipse. Write its equation in standard form 
. Write down its vertices and foci. Calculate the volume of the spindle obtained by rotating the ellipse 
around the 
axis.
is a hyperbola. Write its equation in standard form 
and calculate the equations of their asymptotes.
