Podcast
Questions and Answers
Qual est le valore de $x$ in le equatio $x^2 + x^3 = x^3(1 + x^6)$?
Qual est le valore de $x$ in le equatio $x^2 + x^3 = x^3(1 + x^6)$?
- 1
- 0 (correct)
- 6
- 2
Quanto vale l'integral $ rac{ ext{sen} x + ext{cos} x}{ ext{√sin}^2 x} dx$ inter le limites de $0$ a $ rac{ ext{π}}{3}$?
Quanto vale l'integral $ rac{ ext{sen} x + ext{cos} x}{ ext{√sin}^2 x} dx$ inter le limites de $0$ a $ rac{ ext{π}}{3}$?
- $ rac{ ext{√3}}{2}$ (correct)
- 1
- $ rac{1}{2}$
- $ rac{ ext{π}}{6}$
Qual es le limite de $ ext{e}^{2 - 3x}$ quando $x$ approxima 0?
Qual es le limite de $ ext{e}^{2 - 3x}$ quando $x$ approxima 0?
- 1
- 0
- 2
- e (correct)
Qual es le significato de $ ext{log}(x + 1) - 2 ext{log} x$ in le context de l'integrales?
Qual es le significato de $ ext{log}(x + 1) - 2 ext{log} x$ in le context de l'integrales?
Quot valor es assignate a $ ext{B}$ in le key de responsa dat?
Quot valor es assignate a $ ext{B}$ in le key de responsa dat?
Quotiente es le valor de $ extstyle rac{eta}{eta}$ pro le integration $ extstyle extstyle rac{eta}{eta}$ if $f(x) = 2$ pro $2 ext{ ≤ } x ext{ ≤ } 3$?
Quotiente es le valor de $ extstyle rac{eta}{eta}$ pro le integration $ extstyle extstyle rac{eta}{eta}$ if $f(x) = 2$ pro $2 ext{ ≤ } x ext{ ≤ } 3$?
Qual es le forma correcte del valor del integral $ extstyle extstyle rac{eta}{eta}$ de $ ext{cos } x dx$ in le intervalle $[a, b]$?
Qual es le forma correcte del valor del integral $ extstyle extstyle rac{eta}{eta}$ de $ ext{cos } x dx$ in le intervalle $[a, b]$?
Si $f(x) = 4x^3 - 4$, que exprime $f(2)$?
Si $f(x) = 4x^3 - 4$, que exprime $f(2)$?
Que value representa $f(x)$ pro $x = 1$ dado que $f(x) = 4x^3 - 4$?
Que value representa $f(x)$ pro $x = 1$ dado que $f(x) = 4x^3 - 4$?
Qual es le forma correcte del $f(x)$ si $f'(x) = 4x^3$?
Qual es le forma correcte del $f(x)$ si $f'(x) = 4x^3$?
Quale es le derivative de f(x) = ∫ (0 to x) t sin t dt?
Quale es le derivative de f(x) = ∫ (0 to x) t sin t dt?
Quale es le valore de ∫ (0 to 1) tan^(-1)(2/(1 + x - x^2)) dx?
Quale es le valore de ∫ (0 to 1) tan^(-1)(2/(1 + x - x^2)) dx?
Quale es le resulta de ∫ e^x sec x (1 + tan x) dx?
Quale es le resulta de ∫ e^x sec x (1 + tan x) dx?
Quale es le expression exacte de ∫ (e^(-x) - e^(-x)) dx?
Quale es le expression exacte de ∫ (e^(-x) - e^(-x)) dx?
Quale es le valore de ∫ (e^x sec x (1 + tan x)) dx?
Quale es le valore de ∫ (e^x sec x (1 + tan x)) dx?
Qual es le valore de ∫_{0}^{a} f(x) g(x) dx si f e g satisfac le conditiones specificate?
Qual es le valore de ∫_{0}^{a} f(x) g(x) dx si f e g satisfac le conditiones specificate?
Si f(x) es symmetric in relation a a, qual es le implicantia de f(a-x)?
Si f(x) es symmetric in relation a a, qual es le implicantia de f(a-x)?
Quo significa g(x) + g(a - x) = a in le context de le function g?
Quo significa g(x) + g(a - x) = a in le context de le function g?
In le expression ∫_{0}^{1} f(x).g(x)dx, quale variabile affecta le resultato?
In le expression ∫_{0}^{1} f(x).g(x)dx, quale variabile affecta le resultato?
Qual es le relation inter a e le integral de f(x) si f es symmetric?
Qual es le relation inter a e le integral de f(x) si f es symmetric?
Qual es le valore de a si a(1 + x^2) + b√(1 + x) + C es equal a 3x?
Qual es le valore de a si a(1 + x^2) + b√(1 + x) + C es equal a 3x?
Qual es le resultado del integrale ∫ (sec x sin x) dx?
Qual es le resultado del integrale ∫ (sec x sin x) dx?
Pro le expression ∫ (tan x)/(1 + x^2) dx, qual es le forma correct de solution?
Pro le expression ∫ (tan x)/(1 + x^2) dx, qual es le forma correct de solution?
Qual es le significato del simbolo ∫ in casa de calculus?
Qual es le significato del simbolo ∫ in casa de calculus?
Qual es le resultato del integrale ∫ (1/sin x cos x) dx?
Qual es le resultato del integrale ∫ (1/sin x cos x) dx?
Qual es le resultato del integral $ rac{e^{(x^2 + 1)}}{(x + 1)^2} dx$?
Qual es le resultato del integral $ rac{e^{(x^2 + 1)}}{(x + 1)^2} dx$?
Qual es le forma simplificate del integral $ rac{2x + 5}{
oot{2}{x} + 2x + 5} dx$?
Qual es le forma simplificate del integral $ rac{2x + 5}{ oot{2}{x} + 2x + 5} dx$?
Quo es le resultato del integral $ rac{2 sin(x) + 3 cos(x)}{3 sin(x) + 4 cos(x)} dx$?
Quo es le resultato del integral $ rac{2 sin(x) + 3 cos(x)}{3 sin(x) + 4 cos(x)} dx$?
Qual es le approxima del integral $ rac{x}{(x^2 - a)(x^2 - b)} dx$?
Qual es le approxima del integral $ rac{x}{(x^2 - a)(x^2 - b)} dx$?
Qual es le resultato del integral $
oot{2}{cot(x)} dx$?
Qual es le resultato del integral $ oot{2}{cot(x)} dx$?
Flashcards
Derivata de un integral
Derivata de un integral
Le derivata del function f(x), ubi f(x) es definite como le integral de t sin(t) de 0 a x.
Calcular le integral
Calcular le integral
Le integral de tan⁻¹(2x-1)/(1+x²-x) de 0 a 1.
Integral con exponential e trigonometric functiones
Integral con exponential e trigonometric functiones
Le integral de e^x sec(x)(1+tan(x))dx.
Integral con exponential functiones
Integral con exponential functiones
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Integral con exponential e trigonometric functiones
Integral con exponential e trigonometric functiones
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Integral
Integral
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Integral indefinite
Integral indefinite
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Integral definite
Integral definite
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Methodo de substitution
Methodo de substitution
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Integration per partes
Integration per partes
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Symmetric Function
Symmetric Function
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Skew-Symmetric Function
Skew-Symmetric Function
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Integral of a Symmetric and Skew-symmetric Function
Integral of a Symmetric and Skew-symmetric Function
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Area Under the Curve
Area Under the Curve
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Integral definite con limites infinite (limite superior infinito)
Integral definite con limites infinite (limite superior infinito)
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Integral definite con limites finite
Integral definite con limites finite
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Integral indefinite con radical quadrate
Integral indefinite con radical quadrate
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Integral definite de function trigonometric
Integral definite de function trigonometric
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Integral indefinite de function trigonometric con radical
Integral indefinite de function trigonometric con radical
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Definition de integral definite
Definition de integral definite
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Methodo de Riemann
Methodo de Riemann
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Constante de integration
Constante de integration
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Study Notes
Calculus Problems
-
Problem 1: Given f(x) = ∫₀ˣ t sin t dt, determine f'(x).
- Correct answer: cos x + x sin x
-
Problem 2: Calculate ∫₀¹ tan⁻¹( (2x - 1) / (1 + x - x²) ) dx.
- Correct answer: 0
-
Problem 3: Evaluate ∫ₓ sec x (1 + tan x) dx.
- Correct answer: eˣ sin x + C
-
Problem 4: Find the solution for ∫ (1 / (eˣ - e⁻ˣ)) dx.
- Correct answer: tan⁻¹(eˣ) + C
-
Problem 5: Determine the appropriate substitution for ∫ √(x²(2 + x⁵)) dx.
- Correct answer: x⁶ = t
-
Problem 6: If ∫ (e⁻ˣ - 5e⁻ˣ) / (4eˣ + 5e⁻ˣ) dx = ax + blog|4eˣ + 5e⁻ˣ| + C, then find the values of a and b.
- Correct answer: a = -1/8 , b = 7/8
-
Problem 7: If f(x) = f(a - x) and g(x) + g(a - x) = a on [0, 1], then determine the value of ∫₀ᵃ f(x) g(x) dx
- Correct answer: (a/2) ∫₀ᵃ f(x) dx
-
Problem 8: Given ∫₀¹ [eᵗ / (1 + t)] dt = a , determine the value of ∫₀¹ [eᵗ / (1 + t)² ] dt
- Correct answer: a − (e/2)
-
Problem 9: Find the integral of 1/(sin(x - a) sin(x - b)).
- Correct answer: cosec(b - a) log|sin(x - a)/sin(x - b)| + C
-
Problem 10: Find the values of a and b in the equation ∫ x³√(1 + x²) dx= a(1 + x²)³/² + b√(1 + x²) + C.
- Correct answer: a = 1/3, b = -1
-
Problem 11: Evaluate the following integrals: (i) ∫ sec x sin x dx; (ii) ∫ (1 / (sin x cos² x)) dx
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Problem 12: Find the integral of x² tan⁻¹(x) / (1 + x²) dx
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Problem 13: Calculate the definite integral of ∫ eˣ (x² + 1) / (x + 1)² dx (limits are not specified).
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Problem 14: Calculate the integral of ∫ x / ((x² - a²) (x² - b²)) dx.
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Problem 15: Evaluate the integral of (2x + 5) / √(x² + 2x + 5) dx.
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Problem 16: Prove (in the context of Integration problems and/or Trigonometric substitutions that) ∫ (2 sin x + 3 cos x) / (3 sin x + 4 cos x) dx = (18/25)x + (1/25) log |3 sin x + 4 cos x| + C.
-
Problem 17: Evaluate ∫ cot x dx.
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Problem 18: Find the value of ∫₀∞ (x² / ((x² + a²) (x² + b²) )) dx.
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Problem 19: Given f(x) = {2x + 1, 1 ≤ x ≤ 2 / x² + 1, 2 ≤ x ≤ 3}, determine ∫₁³ f(x) dx.
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Problem 20: Calculate the integral ∫ᵃᵇ cos x dx in terms of a and b using the limit approach.
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Problem 21: Given f'(x) = 4x³ - (3 / x⁴) and f(2) = 0, find f(x).
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Problem 22: Evaluate (x⁸ - 1)¹/³ x⁵ dx
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Problem 23: Evaluate sin³ (2x + 1) dx.
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Problem 24: Evaluate (cos 2x - cos 2a) / (cos x - cos a) dx.
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Problem 25: Find the indefinite integral of (3x - 1) / ( (x - 1)(x - 2)(x - 3)) dx
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Problem 26: Evaluate ∫₀π/2 log(4 + 3 sin x) / (4 + 3 cos x) dx
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Problem 27: Given x² + 1 / x² + x³ = 1/x + 1/x² − 1/x³ (with details stated).
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Problem 28: Evaluate √(x² + 1) [log(x² + 1) − 2 log x] / x⁴ dx.
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Problem 29: Evaluate ∫ₙ /₆ sin x + cos x √(sin 2x) dx.
-
Problem 30: Calculate ∫₀¹ e⁻²⁻³ˣ dx using limit approach.
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Description
Este quiz explora uma variedade de problemas de cálculo, desde integrais definidas até derivadas. Cada problema oferece um cenário único que desafia a compreensão dos conceitos de cálculo. Prepare-se para avaliar suas habilidades e conhecimentos em cálculo através destes problemas testados.
