Integrals
Evaluate the following integral: integral from 0-pi(e^x/pi+cos(x/4))dx
what is:
pie -pi +2sqrt2
Evaluate the following integral:
integral from 0 to pi/3
(sin(x))/(cos^2(x)) dx
What is 1?
The area under the curve f(x) = e^x between −1 ≤ x ≤ 1 is rotated about the x-axis. Find the volume of the resulting solid.
What is
pi/2(e^2-e^-2)
a) Convert (x,y)=(-2,2) to polar coordinates
b) convert (r, theta)= (5,-pi/2) to rectangular coordinates
a) What is (2sqrt2, 3pi.4)
b) (0,-5)
Find the general antiderivative of the function:
f(y)=y(4-3y)^(4/5)
-5/9(4-3y)^(9/5)(4/9-4/14+3y/14)+C
Find integral(2ln(x^2+1)xdx
What is:
(x^2+1)ln(x^2+1)-(x^2+1)+C
Find the area of the shaded region (sin x and cos s picture)
What is 2- sqrt2 ?
Find the volume of the solid obtained by rotating the region enclosed by the graphs of y = x^2 and y = 3x-2 about the axis y = -2. You leave your answer as the sum of fractions (rational numbers) with di§erent denominators.
What is 22pi/15
Also correct: pi(35/3 - 31/5 - 4)
Polar coordinates and polar areas. Find the area of one leaf of the ìfour-petaled roseír = 2 sin 2x?.
What is pi/2
Compute both (1+i)^8 and (1+i)^10
What is 16
What is 32i
Evaluate integral x^2e^xdx
What is e^x(x^2-2x+2)+c
Area between two curves. Find the area of the region enclosed by the curves y = cos x, y = sec2 x,
and x = ?pi/3 .
What is sqrt3/2
Find the volume of a pyramid with rectangular base of sides a and b, and height h.
What is 1/3abh ?
Find the area enclosed by one loop of the polar curve r = 4 sin(2θ)
A = 2pi
If f(x)=x/(x^2+1) what is the average of f on [0,1]?
What is 1/2 ln2 ?
Evaluate the following integral:
integral (1+x)/(1+x^2) dx
What is
arctan(x) +ln(sqrt(1+x^2)) +C
Find the area of the region enclosed by the curves x=y^2 and x = 2y.
What is 4/3
Find the volume of the solid whose base is the unit circle x^2 + y^2 = 1 and whose cross sections perpendicular to the x-axis are squares.
16/3
Find the area of the region inside the curve r = 4 sin 3 theta and outside the circle r = 2
4pi/3 +2sqrt(3)
Find the polar coordinates of the 3 cube roots of 8i
What are:
(2,pi/6)
(2,5pi/6)
(2,3pi/2)
Evaluate integral from 0 to 1
x^5(sqrt(x^3+4))dx
What is 2/45(64-25sqrt(5))
A cat is dropped from a 125 meter skyscraper at time t=0 and begins to fall with acceleration v'(t)=-10 m/s^2
a) What is the speed of the cat after time t?
b) What is the total distance travelled by the cat in the first 4 seconds?
c) How long does it take for the cat to hit the ground?
d) What is the speed of the cat when it hits the ground?
a) 10t
b)80
c)t=5
d)50
A building is constructed on the xy-plane with base x^2+y^2<=4 (that is, the disk of radius 2) with cross-sections perpendicular to the x-axis given by equilateral triangles. Find the volume of the building. (Note that the area of an equilateral triangle with side length s is sort(3)s^2/4)
32/(sqrt(3)
Find the area between the cardioid r=2+2cosx and circle r=6cosx
5pi
Find the area of the region enclosed by the function r(theta)=2+sin(theta) outside of the circle r=3/2
3pi/2 + 15sqrt(3)/8