Calculus Essentials: Integrals, Identities & Sums

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Memorize key rules for calc 1.

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Werdnamos

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Calculus Essentials: Integrals, Identities & Sums


Froggy Jumps Calculus Essentials: Integrals, Identities & SumsOnline version Memorize key rules for calc 1. by Werdnamos 1 What is ∫ e^x dx? a ln\|x\| + C b e^{x+1} + C c e^x + C 2 ∫ sin x dx equals? a -cos x + C b -sin x + C c cos x + C 3 ∫ cos x dx equals? a sin x + C b cos x + C c -sin x + C 4 ∫ 1/x dx is? a ln\|x\| + C b e^x + C c x ln\|x\| + C 5 Power rule: ∫ x^n dx = ? a n x^{n} + C b x^{n+1}/(n+1) + C c x^{n-1}/(n-1) + C 6 ∫ a^x dx equals? a ln(a^x) + C b a^{x+1} + C c a^x/ln a + C 7 Trig identity: sin^2 x + cos^2 x = ? a 0 b tan x c 1 8 Double angle: sin 2x = ? a sin x cos x b 2 sin x cos x c 2 cos x sin x^2 9 Cosine double angle: cos 2x = ? a 2 cos^2 x - 1 b cos^2 x - sin^2 x c 1 - 2 sin^2 x 10 Pythagorean form: 1 + tan^2 x = ? a sec^2 x b cos^2 x c csc^2 x 11 Another form: 1 + cot^2 x = ? a tan^2 x b csc^2 x c sec^2 x 12 Sum of first n integers: ∑_{k=1}^n k = ? a n(n-1)/2 b n(n+1)/2 c n^2/2 13 Sum of squares: ∑_{k=1}^n k^2 = ? a n(n+1)(2n+1)/6 b n(n+1)(n-1)/3 c n(n+1)/2 14 Sum of cubes: ∑_{k=1}^n k^3 = ? a n(n+1)(2n+1)/4 b [n(n+1)/2]^2 c n^3/3 15 Geometric series sum for \|r\|<1: ∑_{k=0}^∞ ar^k = ? a a/(1-r) b a/(1+r) c a r/(1-r) 16 Finite geometric sum: ∑_{k=0}^n ar^k = ? a a(1-r^{n})/(1-r) b a(1+r^{n+1})/(1-r) c a(1-r^{n+1})/(1-r) 17 Riemann sum idea: Δx times sum approximates what? a Derivative b Definite integral c Limit of sequence 18 Which integral corresponds to area under f(x)? a ∫ f(x) dx b ∑ f(x) dx c d/dx f(x) 19 Antiderivative of x^2 is? a x^3/3 + C b x^2/2 + C c 3x^2 + C 20 Antiderivative: ∫ dx/(1+x^2) = ? a arctan x + C b arcsin x + C c ln(1+x^2) + C 21 Trig identity: sin 2x = ? (alternate form) a sin^2 x - cos^2 x b 2 sin x cos x c cos^2 x - sin^2 x 22 Cosine power-reduction form: cos^2 x = ? a (1+cos 2x)/2 b cos 2x c (1-cos 2x)/2 23 Sine power-reduction: sin^2 x = ? a (1+cos 2x)/2 b (1-cos 2x)/2 c sin 2x 24 Integral of sec x tan x is? a ln\|sec x + tan x\| + C b sec x + C c tan x + C 25 Integral of csc x cot x is? a ln\|csc x - cot x\| + C b csc x + C c -csc x + C 26 Sum of first n natural numbers alternative form? a n(n-1)/2 b n^2/2 c n(n+1)/2 27 Common derivative of e^{ax} is? a e^{ax} b e^{ax}/a c a e^{ax} 28 Derivative of ln x is? a 1/x^2 b 1/x c x 29 Integral of sec^2 x is? a ln\|sec x\| + C b sec x + C c tan x + C 30 Derivative of tan x is? a 1/cos^2 x b sec^2 x c cos^2 x 31 Sum of cubes formula: ∑ k^3 equals? a n(n+1)(2n+1)/6 b n^2(n+1)^2/4 c [n(n+1)/2]^2

Calculus Essentials: Integrals, Identities & Sums

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Calculus Essentials: Integrals, Identities & SumsOnline version

by Werdnamos

What is ∫ e^x dx?

∫ sin x dx equals?

∫ cos x dx equals?

∫ 1/x dx is?

Power rule: ∫ x^n dx = ?

∫ a^x dx equals?

Trig identity: sin^2 x + cos^2 x = ?

Double angle: sin 2x = ?

Cosine double angle: cos 2x = ?

Pythagorean form: 1 + tan^2 x = ?

Another form: 1 + cot^2 x = ?

Sum of first n integers: ∑_{k=1}^n k = ?

Sum of squares: ∑_{k=1}^n k^2 = ?

Sum of cubes: ∑_{k=1}^n k^3 = ?

Geometric series sum for |r|<1: ∑_{k=0}^∞ ar^k = ?

Finite geometric sum: ∑_{k=0}^n ar^k = ?

Riemann sum idea: Δx times sum approximates what?

Which integral corresponds to area under f(x)?

Antiderivative of x^2 is?

Antiderivative: ∫ dx/(1+x^2) = ?

Trig identity: sin 2x = ? (alternate form)

Cosine power-reduction form: cos^2 x = ?

Sine power-reduction: sin^2 x = ?

Integral of sec x tan x is?

Integral of csc x cot x is?

Sum of first n natural numbers alternative form?

Common derivative of e^{ax} is?

Derivative of ln x is?

Integral of sec^2 x is?

Derivative of tan x is?

Sum of cubes formula: ∑ k^3 equals?