Integration By "Party"
Definite Integrals Rock
A Substitute is Required
Fun With Trig
Potpourri
100
Evaluate Int x ln(x) dx.
What is 1/2 x^2ln(x) - 1/4 x^2 + C
100
Evaluate Int((x + 2x^2)/x,x,1,2)
What is 4
100
Evaluate Int 4x^3 / sqrt(x^4 + 9) dx
What is 2 sqrt(x^4 + 9) + C
100
Eval Int sin(x)/cubeRt(cos(x)) dx
What is -3/2 (cos(x))^(2/3) + C
100
Evaluate the improper integral Int(e^(-2x),x,1,infinity)
What is 1/2 e^-2
200
Evaluate Int (x + 2) e^(2x + 1) dx
What is 1/2(x + 2)e^(2x + 1) - 1/4 e^(2x + 1) + C
200
Evaluate Int(1/(x lnx),x,e,e^2)
What is ln2
200
Evaluate Int tan(x) sec^4(x) dx
What is 1/4 sec^4(x) + C or 1/4 tan^4(x) + 1/2 tan^2(x) + C
200
Evaluate Int sin(x) cos(cos(x)) dx
What is -sin(cos(x)) + C
200
Evaluate the improper Integral Int(1/x^4,x,-2,3)
What is Divergent
300
Evaluate Int x^2 cos(x) dx
What is x^2 sin(x) + 2x cos(x) - 2sin(x) + C
300
Evaluate Int(x e^x,x,0,2)
What is e^2 + 1
300
Evaluate Int 1/(xsqrt(lnx)) dx
What is 2 sqrt(lnx) + C
300
Evaluate Int tan^2(x)sec^4(x) dx
What is 1/5 tan^5(x) + 1/3 tan^3(x) + C
300
The arc length of y = ln(secx) for [0,pi/4].
What is ln(sqrt(2) + 1)
400
Evaluate Int e^sqrt(x) dx
What is 2e^sqrt(x) * sqrt(x) - 2 e^sqrt(x) + C
400
Evaluate Int(cos(e^(x^2)),x,sin(pi/2),lne)
What is 0
400
Evaluate Int x sqrt(x - 5) dx
What is 2/5 (x - 5)^(5/2) + 10/3 (x - 5)^(3/2) + C
400
Evaluate Int (1 + cos(x))/sin(x) dx
What is ln(csc(x) - cot(x)) + ln(sin(x)) + C OR ln|1-cosx| + C
400
Set up an integral to find the surface area formed by rotating f(x) = sin(x), on the interval [0,pi] about the x-axis.
What is 2pi Int(sin(x)sqrt(1 + cos^2(x)),x,0,pi)
500
Evaluate Int e^x sin(3x) dx
What is 1/10 e^x sin(3x) - 3/10 e^x cos(3x) + C
500
Evaluate Int(x e^sin(x^2),x,-pi,pi)
What is 0
500
Evaluate Int sqrt(16 - x^2) dx
What is 1/2 x sqrt(16 - x^2) + 8 arcsin(x/4) + C
500
Evaluate Int x tan^2(x) dx
What is x tan(x) - x^2/2 + ln(cos(x)) + C
500
Find the center of mass for the region enclosed by y = 4 - x^2 and the x-axis.
What is (0,8/5)
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