AP Calculus AB Formulas Flashcards
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Questions and Answers

What is the derivative of (sin x)?

cos x

What is the derivative of (cos x)?

-sin x

What is the derivative of (tan x)?

sec^2 x

What is the derivative of (sec x)?

<p>sec x tan x</p> Signup and view all the answers

What is the derivative of (csc x)?

<p>-csc x cot x</p> Signup and view all the answers

What is the derivative of (cot x)?

<p>-csc^2 x</p> Signup and view all the answers

What is the derivative of (arcSin u)?

<p>u' / (1 - u^2)^{1/2}</p> Signup and view all the answers

What is the derivative of (arcCos x)?

<p>-u' / (1 - u^2)^{1/2}</p> Signup and view all the answers

What is the derivative of (arcTan x)?

<p>u' / (u^2 + 1)</p> Signup and view all the answers

What is the derivative of (arcSec x)?

<p>u' / |u| (u^2 - 1)^{1/2}</p> Signup and view all the answers

What is the derivative of (arcCsc x)?

<p>-u' / |u| (u^2 - 1)^{1/2}</p> Signup and view all the answers

What is the derivative of (arcCot x)?

<p>-u' / (u^2 + 1)</p> Signup and view all the answers

What is the derivative of (Ln u)?

<p>u' / u</p> Signup and view all the answers

What is the derivative of (e^(u))?

<p>u' e^(u)</p> Signup and view all the answers

What is the integral of x^n dx?

<p>(x^(n+1)) / (n+1) + C</p> Signup and view all the answers

What is the integral of 1/x dx?

<p>Ln x + C</p> Signup and view all the answers

What is the integral of 1/x^2 dx?

<p>-1/x + C</p> Signup and view all the answers

What is the integral of dx/(x + b)?

<p>Ln |x + b| + C</p> Signup and view all the answers

What is the integral of sin x dx?

<p>-cos x + C</p> Signup and view all the answers

What is the integral of sin(ax) dx?

<p>(-cos(ax)) / a + C</p> Signup and view all the answers

What is the integral of cos x dx?

<p>sin x + C</p> Signup and view all the answers

What is the integral of cos(ax) dx?

<p>(sin(ax)) / a + C</p> Signup and view all the answers

What is the integral of tan x dx?

<p>{ Ln |sec x| + C - Ln |cos x| + C }</p> Signup and view all the answers

What is the integral of sec x dx?

<p>Ln |sec x + tan x| + C</p> Signup and view all the answers

What is the integral of sec x tan x dx?

<p>sec x + C</p> Signup and view all the answers

What is the integral of sec^2 x dx?

<p>tan x + C</p> Signup and view all the answers

What is the integral of e^x dx?

<p>e^x + C</p> Signup and view all the answers

What is the integral of e^(ax) dx?

<p>(1/a) e^(ax) + C</p> Signup and view all the answers

What is the integral of dx/(x + b)?

<p>Ln |x + b| + C</p> Signup and view all the answers

What is the integral of dx/(ax + b)?

<p>(1/a) Ln |ax + b| + C</p> Signup and view all the answers

What does the First Fundamental Theorem of Calculus state?

<p>ʃab f(x) dx = F(b) - F(a); ʃab f '(x) dx = f(b) - f(a)</p> Signup and view all the answers

What does the Second Fundamental Theorem of Calculus state?

<p>F(x) = ʃax f(t) dt; F'(x) = f(x)</p> Signup and view all the answers

What is the Trapezoid Rule for approximating integrals?

<p>ʃab f(x) dx ~= ((b-a)/2n) [A + 2B + 2C + 2D + E] if n=4</p> Signup and view all the answers

What is the formula for Right Riemann Sum?

<p>(w1 * B) + (w2 * C) + (w3 * D) + (w4 * E) [A,E]</p> Signup and view all the answers

What is the formula for Left Riemann Sum?

<p>(w1 * A) + (w2 * B) + (w3 * C) + (w4 * D) [A,E]</p> Signup and view all the answers

What is the formula for Midpoint Riemann Sum?

<p>(w1 * A) + (w2 * B) + (w3 * C) + (w4 * D) + (w4 * D) [A,E]</p> Signup and view all the answers

Study Notes

Derivadas de Funções Trigonométricas

  • A derivada de (sin x) è cos x.
  • A derivada de (cos x) è -sin x.
  • A derivada de (tan x) è sec^2 x.
  • A derivada de (sec x) è sec x * tan x.
  • A derivada de (csc x) è -csc x * cot x.
  • A derivada de (cot x) è -csc^2 x.

Derivadas de Funções Inversas

  • A derivada de (arcSin u) è u' / √(1 - u^2).
  • A derivada de (arcCos u) è -u' / √(1 - u^2).
  • A derivada de (arcTan u) è u' / (u^2 + 1).
  • A derivada de (arcSec u) è u' / |u|√(u^2 - 1).
  • A derivada de (arcCsc u) è -u' / |u|√(u^2 - 1).
  • A derivada de (arcCot u) è -u' / (u^2 + 1).

Derivadas de Funções Exponenciais e Logarítmicas

  • A derivada de (Ln u) è u' / u.
  • A derivada de (e^(u)) è u' * e^(u).

Integrais de Potências e Funções Comuns

  • A integral de x^n dx è (x^(n+1)) / (n+1) + C, para n ≠ -1.
  • A integral de 1/x dx è Ln |x| + C.
  • A integral de 1/x^2 dx è -1/x + C.

Integrais Trigonométricas

  • A integral de sin x dx è -cos x + C.
  • A integral de sin(ax) dx è (-cos(ax)) / a + C.
  • A integral de cos x dx è sin x + C.
  • A integral de cos(ax) dx è (sin(ax)) / a + C.
  • A integral de tan x dx è Ln |sec x| + C.
  • A integral de sec x dx è Ln |sec x + tan x| + C.
  • A integral de sec x * tan x dx è sec x + C.
  • A integral de sec^2 x dx è tan x + C.

Integrais Exponenciais

  • A integral de e^x dx è e^x + C.
  • A integral de e^(ax) dx è (1/a)e^(ax) + C.

Integrais de Funções Racionais

  • A integral de dx / (x + b) è Ln |x + b| + C.
  • A integral de dx / (ax + b) è (1/a)Ln |ax + b| + C.

Teoremas Fundamentais do Cálculo

  • O Primeiro Teorema Fundamental do Cálculo: ʃ(a to b) f(x) dx = F(b) - F(a), onde F é uma antiderivada de f.
  • O Segundo Teorema Fundamental do Cálculo: Se F(x) = ʃ(a to x) f(t) dt, então F'(x) = f(x).

Regras de Aproximação para Integrais

  • A Regra do Trapézio: ʃ(a to b) f(x) dx ≈ ((b - a)/2n) [A + 2B + 2C + 2D + E], com n=4.
  • A Regra da Soma à Direita (Right RAM): (w1 * B) + (w2 * C) + (w3 * D) + (w4 * E), onde w é a distância do ponto x anterior.
  • A Regra da Soma à Esquerda (Left RAM): (w1 * A) + (w2 * B) + (w3 * C) + (w4 * D).
  • A Regra do Ponto Médio (Midpoint RAM): (w1 * A_m) + (w2 * B_m) + (w3 * C_m) + (w4 * D_m), utilizando as coordenadas x e y no meio de cada região.

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Iste quiz presenta un collection de flashcards pro le formulas essential in le cursus AP Calculus AB. Cada card presenta un derivativa e su forma correspondente. Testa tu cognoscentia e memorie de le formulas con iste exercitios util.

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