REVIEW GAME :)

Cylindrical Shells

100

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

One integral instead of two

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

300

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

4pi/3

400

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

32pi/3

Parts : Basic +Complex

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)

200

∫ x^3 ln x dx

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

300

∫sin x ln(cos x) dx

−cos x ln(cos x) + cos x + C

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

Random

100

What was the highest grade on the final?

 99

200

what is the integral of d(x)

x+c

300

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

Fermats's last theorem.

400

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

Decimal point

Rapid Repeated by Parts

100

 ∫x³e^x dx

x³e^x−3x²e^x+6xe^x−6e^x+C

200

∫(log x)² dx

x(log x)² − 2x log x + 2x + C

300

∫e^2x sin(3x) dx

1/13 e^2x (2 sin(3x) − 3 cos(3x)) + C.

400

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

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

Partial Fraction: Basic + complex

100

∫1 / 2x³ + x ² − x dx

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

200

∫ 1/ x ² − 4 dx

1/4 ln (|x−2| / |x+2|) + C

300

∫(2x − 1) / (x ² − x − 6) dx

ln |x ² − x − 6| + C

400

∫(2x + 3)/ (x ² − 9) dx

1/2 ln |x + 3| + 3/2 ln |x − 3| + C