Calc 2 Exam 1

Area between 2 curves: ∫ [f(x)-g(x)](dx) or (dy)

Area between 2 curves (dx): difference between right - left (left value is lower bound)

Area between 2 curves (dy): difference between top and bottom (bottom value is lower bound)

Disk Method: π ∫ [R(x)²] (dx) or (dy) = V

Washer Method: π ∫ [R(x)² - r(x)²] (dx) or (dy) = V

Shell Method: 2π ∫ r(h) (dx) or (dy)

Dish and Washer rotation about x-axis: (dx)

Disk and Washer rotation about y-axis: (dy)

Shell method rotation about x-axis: (dy)

Shell method rotation about y-axis: (dx)

Shell method R(x)

Shell method height (dx): Difference between top and bottom

Shell method height (dy): Difference between right and left

Shell method radius: Distance from axis of rotation

Radius: | x - axis | or | y - axis |

Radius if x or y > axis of rotation: r = x - axis

Radius if x or y < axis of rotation: r = axis - x

International Units for Force: N

International Units for Displacement: m

International Units for Work: J

International Units for Spring Constant: N/m

US Units for Force: lb

US Units for Displacement: ft

US Units for Work: ft-lb

US Units for Spring Constant: lb/ft

Hookes Law: F(x) = kx

Work Integral: W = ∫ F(x) (dx)

Pythagorean Identities sin/cos: sin²x+cos²x=1

Pythagorean Identities sec/tan: sec²x-tan²x=1

Pythagorean Identites csc/cot: csc²x-cot²x=1

sin(2x): 2sinxcosx

sin²x: 1-cos(2x)/2

cos²x: 1+cos(2x)/2

tan²x: 1-cos(2x)/1+cos(2x)

Trig Sub sqrt(a²-x²): x=asin(theta)

Trig Sub sqrt(a²+x²): x=atan(theta)

Trig Sub sqrt(x²-a²): x=asec(theta)

∫1/(a²+x²): 1/a arctan(x/a) + C

∫ x/(a²+x²): u-sub (pattern)

∫ 1/(ax+b): 1/a ln|ax+b| + C

∫secx = ln| secx + tanx| + C

∫tanx = ln| secx | + C