CALC 2 EXAM WITH VERIFIED CONTENT #17
Integration by parts formula - correct answer ∫udv= uv-∫vdu
LIATE (to choose U for integration by parts) - correct answer
Logarithmic/Inverse/Algebraic/Trigonometric/Exponential
Half Angle Formula for cos²x - correct answer cos²x=(1+cos2x)/2
Half Angle Formula for sin²x - correct answer sin²x=(1-cos2x)/2
Trig identity involving sin and cos - correct answer sin²x + cos²x = 1
Trig identity involving tan and sec - correct answer tan²x + 1 = sec²x
Trig identity involving cot and csc - correct answer 1 + cot²x = csc²x
Sinx/cosx= - correct answer tanx
Cosx/sinx= - correct answer cotx
∫sinⁿxcosⁿxdx if cosine is odd...u-sub is... - correct answer sinx
∫sinⁿxcosⁿxdx if sine is odd...u-sub is... - correct answer cosx
∫sinⁿxcosⁿxdx if both are odd...u-sub is... - correct answer either cosx or sinx
∫sinⁿxcosⁿxdx if both are even...u-sub is... - correct answer no u-sub! Use half-angle
formulas
∫tanⁿxsecⁿxdx if secant is even...u-sub is... - correct answer tanx
∫tanⁿxsecⁿxdx if tangent is odd...u-sub is... - correct answer secx
Trig sub for √(a² - x²) - correct answer x=asinθ
Trig sub for √(a² + x²) - correct answer x=atanθ
Trig sub for √(x² - a²) - correct answer x=asecθ
∫1/x dx - correct answer ln|x| + C
∫e^x dx - correct answer = e^x + C
∫b^x dx - correct answer b^x/lnb
Integration by parts formula - correct answer ∫udv= uv-∫vdu
LIATE (to choose U for integration by parts) - correct answer
Logarithmic/Inverse/Algebraic/Trigonometric/Exponential
Half Angle Formula for cos²x - correct answer cos²x=(1+cos2x)/2
Half Angle Formula for sin²x - correct answer sin²x=(1-cos2x)/2
Trig identity involving sin and cos - correct answer sin²x + cos²x = 1
Trig identity involving tan and sec - correct answer tan²x + 1 = sec²x
Trig identity involving cot and csc - correct answer 1 + cot²x = csc²x
Sinx/cosx= - correct answer tanx
Cosx/sinx= - correct answer cotx
∫sinⁿxcosⁿxdx if cosine is odd...u-sub is... - correct answer sinx
∫sinⁿxcosⁿxdx if sine is odd...u-sub is... - correct answer cosx
∫sinⁿxcosⁿxdx if both are odd...u-sub is... - correct answer either cosx or sinx
∫sinⁿxcosⁿxdx if both are even...u-sub is... - correct answer no u-sub! Use half-angle
formulas
∫tanⁿxsecⁿxdx if secant is even...u-sub is... - correct answer tanx
∫tanⁿxsecⁿxdx if tangent is odd...u-sub is... - correct answer secx
Trig sub for √(a² - x²) - correct answer x=asinθ
Trig sub for √(a² + x²) - correct answer x=atanθ
Trig sub for √(x² - a²) - correct answer x=asecθ
∫1/x dx - correct answer ln|x| + C
∫e^x dx - correct answer = e^x + C
∫b^x dx - correct answer b^x/lnb
