Calculus II and Multivariable Calculus: Infinite Sums With Finite Answers
From series that converge to π²/6 and a horn you can fill but never paint, to gradients, flux and the theorems that tie them together.
Calculus II and Multivariable Calculus · 50 questions
Try 3 questions
1. Integration by parts is the reverse of which differentiation rule?
- The chain rule
- The product rule
- The quotient rule
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Answer: The product rule
Integrating (uv)′ = u′v + uv′ and rearranging gives ∫u dv = uv − ∫v du.
2. Which substitution makes ∫ 2x · cos(x²) dx easy?
- u = 2x
- u = cos x
- u = x²
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Answer: u = x²
With u = x², du = 2x dx appears exactly in the integrand, leaving ∫cos u du = sin(x²) + C. Substitution undoes the chain rule.
3. What is true of an antiderivative of the bell-curve function e^(−x²)?
- It is simply e^(−x²) divided by −2x
- It is e^(−x²) multiplied by −2x
- No formula in elementary functions exists
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Answer: No formula in elementary functions exists
It provably cannot be written with polynomials, roots, exponentials, logs and trig functions, so it is given its own name, the error function.
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