Run of the Mill
Find the average value of the function, on the interval [0,2]
f(x)=2+3x
What is 5
What is the area of the region bounded by:
y=x^3, y=0, x=1, x=3
What is
20
Find the volume of the solid whose base is bounded by the functions
y=x^2
and
y=x^5
whose cross sections perpendicular to the x-axis are rectangles with a height of 3.
What is
1/2
Find the volume of a solid obtained by rotating the region bounded by the curves
y=sqrt(x-2), y=0,& x=6
about the x-axis.
What is
8pi
Find the average value of f(x) on the interval [4,9]
f(x)=sqrtx
What is
38/15
Find the average value of the function on the interval given
f(x)=sin3x [0,pi/3]
What is
2/pi
Find the area of the region bounded by:
y=4x-x^2
y=0, x=1, x=3
What is 22/3
Find the volume of a solid that has a base bounded by
y=1-x^2,
and the x-axis, whose cross sections perpendicular to the x-axis are squares.
What is
6/5
Find the volume of the solid obtained by rotating the region bounded by
y=-x^2+1, x=0, & x=1
about the x-axis.
What is
(8pi)/15
A kite is flying 100 feet above the ground at the end of a string 125 feet long. The person flying the kite lets out the string at a rate of 1 ft/sec. If the kite remains 100 feet above the ground, find how fast is it's horizontal distance from the person increases.
What is
5/3
feet/sec
Find the average value of the following on the given interval.
f(x)=sqrt(4-x^2) [-2,2]
What is
pi/2
Find the area of the region bounded by:
y=1/(1+x^2)
y=0, x=-1,x=1
What is
1/2 pi
Find the volume of the solid whose base is bounded by the x-axis and the curve
y=1-x^2
Each cross section of the solid perpendicular to the x-axis is an equilateral triangle with one side lying on the base.
What is
(3sqrt3)/5
What is the volume of the solid generated by revolving the region bounded by
y=0, x=4, y=sqrtx
about the y-axis.
What is
(128pi)/5
Find the area of the region bounded by:
y=tanx, x=0 , and x=pi/4
What is
1/2 ln2
Find the average value of f(x) on the interval [0,5], and state at how many points in the interval does f(x) have this value.
f(x)=xsqrt(25-x^2)
What is
25/3
it occurs twice
Find the area of the region bounded by:
y=6x-x^2 and y=x^2-2x
What is
64/3
Find the volume of a solid whose base is bounded by the x-axis and
y=1-x^2
Each cross section perpendicular to the y-axis is an isosceles right triangle with the hypotenuse lying on the base.
What is
1/2
Find the volume of the solid obtained by rotating the region bounded by the curve
y=x^3, y=0,& x=1
about the line
x=2
What is
(3pi)/5
Express the expression below as the limit of a sum:
int_1^4(2x-1/x^2)dx
What is
lim_(n->oo)sum_(i=1)^n[2(1+(3i)/n)-1/(1+(3i)/n)^2]3/n
A particle is moving along a straight line so that its velocity at time t is v(t)=3t2. Find the time t during the interval 0<t<3 its velocity is the same as its average velocity over the entire interval.
What is
t=sqrt3
Find the area common to the circles:
x^2+y^2=4, and x^2+y^2=4x
What is
Find the volume of a solid whose base is bounded by
y=4-x^2
and the x-axis, and whose cross section perpendicular to the x-axis is a semi-circle.
What is
(64pi)/15
Find the volume of the solid generated by revolving the region bounded by
y=x^2, y=4x-x^2
around the line
y=6
What is
(64pi)/3
Find the solution to the differential equation
y'=x^2y
that satisfies the initial of [0,8]
What is
y=8e^(x^3/3)