Cylindrical Shells
Parts : Basic +Complex
Random
Rapid Repeated by Parts
Partial Fraction: Basic + complex
100

What is the benefit of using the shell method over the disc method?

One integral instead of two
100

What is the acronym used to select u and dv (and what does each letter stand for)

LIATE (log, inv trig, agl, trig, expon)

100

What was the highest raw score grade on the final?

 83

100


 ∫x3ex dx

x3ex−3x2ex+6xex−6ex+C

100

∫1 / 2x3 + x 2 − x dx

2/3 ln |2x − 1/3 ln |x + 1| − ln |x| + C

200

Find the volume of the solid obtained by rotating about the y-axis the region between y=x and y=x^2.

pi/6

200

∫ x^3 ln x dx

(x^4)/4 (lnx)- x^4/16 +c

200

what is the integral of d(x)

x+c

200

∫(log x)2 dx

x(log x)2 − 2x log x + 2x + C

200

∫ 1/ (x 2 − 4) dx

1/4 ln (|x−2| / |x+2|) + C

300

x^2 +( y - 1)^2 = 1, about the y axis.

4pi/3

300

∫sin x ln(cos x) dx

−cos x ln(cos x) + cos x + C

300

What theorem was trying to be proved in the documentary we watched in class?

Fermats's last theorem.

300

∫e2x sin(3x) dx

1/13 e2x (2 sin(3x) − 3 cos(3x)) + C.

300

∫(2x − 1) / (x 2 − x − 6) dx

ln |x 2 − x − 6| + C

400

y = -x^2 + 7, y = x^2+5, about axis x=2

32pi/3

400

∫ x^2 √(x −1) dx

((2x^2)(x-1)^(3/2)) over 3 - (8x(x-1)^(5/2)) over 15 + 16(x-1)^(7/2) over 105 + C

400

What mathematical symbol can be put between 5 and 9, to get a number bigger than 5 and smaller than 9?

Decimal point

400

Find the anti-derivative of x 2 sin(x)

−x 2 cos(x) + 2x sin(x) + 2 cos(x) + C

400

∫(2x + 3)/ (x 2 − 9) dx

1/2 ln |x + 3| + 3/2 ln |x − 3| + C

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