Math 2414 Final Exam 1 Questions And
Complete Solutions (Verified Solutions) 2026
Area between curves - CORRECT ANSWER -dy: ∫ R-L
dx: ∫ T-B
Disc Method Volume - CORRECT ANSWER -V = pi ∫ r^2 dx
Shell Method Volume - CORRECT ANSWER -V = 2pi ∫ x* (f(x)-g(x)) dx -> T-B
V= 2pi ∫ y* (f(y)-g(y)) dy -> R-L
Integration by parts - CORRECT ANSWER -∫ uv' dv = uv - ∫ u'v
L: Log
I: Inverse Trig
P: Polynomials
E: Exponentials
T: Trig
Sin^2(x) = - CORRECT ANSWER -(1-cos2x)/2
Cos^2(x) = - CORRECT ANSWER -(1 + cos2x)/2
sec^2x = - CORRECT ANSWER -1 + tan^2x
∫ tanx = - CORRECT ANSWER -ln | sec(x) |
∫ secx = - CORRECT ANSWER -ln | sec(x) + tan(x) |
Complete Solutions (Verified Solutions) 2026
Area between curves - CORRECT ANSWER -dy: ∫ R-L
dx: ∫ T-B
Disc Method Volume - CORRECT ANSWER -V = pi ∫ r^2 dx
Shell Method Volume - CORRECT ANSWER -V = 2pi ∫ x* (f(x)-g(x)) dx -> T-B
V= 2pi ∫ y* (f(y)-g(y)) dy -> R-L
Integration by parts - CORRECT ANSWER -∫ uv' dv = uv - ∫ u'v
L: Log
I: Inverse Trig
P: Polynomials
E: Exponentials
T: Trig
Sin^2(x) = - CORRECT ANSWER -(1-cos2x)/2
Cos^2(x) = - CORRECT ANSWER -(1 + cos2x)/2
sec^2x = - CORRECT ANSWER -1 + tan^2x
∫ tanx = - CORRECT ANSWER -ln | sec(x) |
∫ secx = - CORRECT ANSWER -ln | sec(x) + tan(x) |
