Indefinite Integrals
Find the general indefinite integral. (Use C for the constant of integration.)
int(4x^3 + 8x + 7)dx
x^4+4x^2+7x+C
Evaluate the integral.
int_0^1(x^2+2x-3)dx
-5/3
Volume of a rectangular box
V=lwh
Formula relating work, force and distance.
W=Fd
Find the average value of the function
f(x)=1+x^2
on the interval [-1,2]
2
Find the general indefinite integral. (Use C for the constant of integration.)
int(x^1.4+9x^3.5)dx
5/12x^2.4+2x^4.5+C
Evaluate the integral.
int_1^3(x^2+2x-3)dx
32/3
Volume of a circular cylinder
V=pir^2h
The amount of work done in lifting a 20-lb weight 6 feet off the ground.
120 ft-lb
Find the average value of the function
f(x)=sqrtx
on the interval [0,9]
2
Find the general indefinite integral. (Use C for the constant of integration.)
int(12x^3+cos(x))dx
3x^4+sin(x)+C
Evaluate the integral.
int_1^4 sqrt x \ dx
14/3
Volume of a sphere
V=4/3pir^3
The amount of work done in hoisting a 1,500-lb grand piano from the ground to the fifth floor, 70 feet above the ground.
105,000 ft-lb
Find the average value of the function
f(x)=4 cos(x)
on the interval
[-pi/2,pi/2]
8/pi
Find the general indefinite integral. (Use C for the constant of integration.)
int(sec(x)tan(x)+10x^4+csc^2(x))dx
sec(x)+2x^5-cot(x)+C
Evaluate the integral.
int_4^9 sqrt x \ dx
38/3
Volume of a cone
V=1/3pir^2h
The amount of work done in lifting a 1.2-kg book off the floor to put it on a desk that is 0.5 m high.
W=Fd=(11.76N)(0.5m)=5.88 J
Find the average value of the function
f(x)=1/x^2
on the interval [1,5]
1/5
FREE POINTS
FREE POINTS
Evaluate the integral.
int_0^1 (x+3)(x-4) \ dx
-73/6
The volume of a cone is what fraction of the volume of a circular cylinder
One third
The amount of work done in lifting 125 kg from 1.0 m to 2.5 m above the ground.
W=Fd=(1225N)(1.5m)=1837.5 J
Find the average value of the function
f(x)=e^(1/x) / x^2
on the interval [2,9]
1/7(e^(1/2) - e^(1/9))