CALCULUS 2 – EXAM WITH SOLUTIONS -14

CALCULUS 2 – EXAM WITH SOLUTIONS #14
Substitution - correct answer integral (f(g(x)) g'(x) dx) = integral (f(u) du)
U=g(x)
Du=g'(x)dx

Integration by parts - correct answer integral (u dv) = uv - integral (v du)

LIPET - correct answer log
Inverse
Polynomial/power
Exponential
Trig

Powers of sine/cosine - correct answer integral (sin^nx cos^mx) dx

Integral (sin^nx cos^mx) dx
N odd - correct answer u=cosx
Du=-sinx dx

Integral (sin^nx cos^mx) dx
M odd - correct answer u=sinx
Du=cosx dx

Integral (sin^nx cos^mx) dx
Both are odd - correct answer either

Integral (sin^nx cos^mx) dx
Both even - correct answer half angle

Powers of secant/tangent - correct answer integral (tan^mx sec^nx) dx

Integral (tan^mx sec^nx) dx
M odd - correct answer u=secx
Du=secxtanx dx

Integral (tan^mx sec^nx) dx
N even - correct answer u=tanx
Du=sec^2x dx

Products - correct answer product to sum

Sqrt(x^2+a^2) - correct answer atan(theta)=x
Asec^2(theta) d(theta) = dx
Hypotenuse is the radical