CALCULUS 2 FINAL LATEST
EXAM - MATH 220,
CALCULUS II, REVIEW
EQUATIONS AND DEFS
FOR FINAL EXAM
Arc Length Formula - ANSWERS-₀∫ⁿ [1 + ƒ'(x)²]
Volume of Solid of Revolution (Disk) - ANSWERS-π ₀∫ⁿ ƒ(x)²
Volume of Solid of Revolution (Washer) - ANSWERS-π ₀∫ⁿ ƒ(x)² - g(x)²
Surface Area of Solid of Revolution - ANSWERS-2π ₀∫ⁿ ƒ(x) √[1 +
ƒ'(x)²]
* arc length × f(x) × 2π
Work Required - ANSWERS-₀∫ⁿ F × D
Work Required (Spring/Chain/Rope) - ANSWERS-₀∫ⁿ kx
*k = spring constant
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, CALCULUS 2 FINAL LATEST
EXAM - MATH 220,
CALCULUS II, REVIEW
EQUATIONS AND DEFS
FOR FINAL EXAM
Work Required (Pumping Fluids) - ANSWERS-₀∫ⁿ
(density)(volume)(distance)
*ie. ₀ ∫ ² (62.4)(25π dy)(9-y)
Integration by Parts - ANSWERS-∫ u dv = uv - ∫ v du
*for u, pick derivable (gets smaller) function
*for dv, pick integratable (gets smaller) function
Volume of Solid by Slicing - ANSWERS-₀∫ⁿ Α(x), if ⊥ x-axis
*Α(y) if ⊥ y-axis
*ie. ∫ (x)² dx, ƒ(x) = x², ⊥ x-axis
or
∫ (√y)² dy, ⊥ y-axis
ƒ'(sin⁻¹ x)
END OF
PAGE
2
EXAM - MATH 220,
CALCULUS II, REVIEW
EQUATIONS AND DEFS
FOR FINAL EXAM
Arc Length Formula - ANSWERS-₀∫ⁿ [1 + ƒ'(x)²]
Volume of Solid of Revolution (Disk) - ANSWERS-π ₀∫ⁿ ƒ(x)²
Volume of Solid of Revolution (Washer) - ANSWERS-π ₀∫ⁿ ƒ(x)² - g(x)²
Surface Area of Solid of Revolution - ANSWERS-2π ₀∫ⁿ ƒ(x) √[1 +
ƒ'(x)²]
* arc length × f(x) × 2π
Work Required - ANSWERS-₀∫ⁿ F × D
Work Required (Spring/Chain/Rope) - ANSWERS-₀∫ⁿ kx
*k = spring constant
END OF
PAGE
1
, CALCULUS 2 FINAL LATEST
EXAM - MATH 220,
CALCULUS II, REVIEW
EQUATIONS AND DEFS
FOR FINAL EXAM
Work Required (Pumping Fluids) - ANSWERS-₀∫ⁿ
(density)(volume)(distance)
*ie. ₀ ∫ ² (62.4)(25π dy)(9-y)
Integration by Parts - ANSWERS-∫ u dv = uv - ∫ v du
*for u, pick derivable (gets smaller) function
*for dv, pick integratable (gets smaller) function
Volume of Solid by Slicing - ANSWERS-₀∫ⁿ Α(x), if ⊥ x-axis
*Α(y) if ⊥ y-axis
*ie. ∫ (x)² dx, ƒ(x) = x², ⊥ x-axis
or
∫ (√y)² dy, ⊥ y-axis
ƒ'(sin⁻¹ x)
END OF
PAGE
2
