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 $x^2 + x^3 = x^3(1 + x^6)$?
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}$?
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?
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?
Signup and view all the answers
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?
Signup and view all the answers
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 $2 ext{ ≤ } x ext{ ≤ } 3$?
Signup and view all the answers
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 $[a, b]$?
Signup and view all the answers
Si $f(x) = 4x^3 - 4$, que exprime $f(2)$?
Si $f(x) = 4x^3 - 4$, que exprime $f(2)$?
Signup and view all the answers
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 $f(x) = 4x^3 - 4$?
Signup and view all the answers
Qual es le forma correcte del $f(x)$ si $f'(x) = 4x^3$?
Qual es le forma correcte del $f(x)$ si $f'(x) = 4x^3$?
Signup and view all the answers
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?
Signup and view all the answers
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?
Signup and view all the answers
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?
Signup and view all the answers
Quale es le expression exacte de ∫ (e^(-x) - e^(-x)) dx?
Quale es le expression exacte de ∫ (e^(-x) - e^(-x)) dx?
Signup and view all the answers
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?
Signup and view all the answers
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?
Signup and view all the answers
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)?
Signup and view all the answers
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?
Signup and view all the answers
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?
Signup and view all the answers
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?
Signup and view all the answers
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?
Signup and view all the answers
Qual es le resultado del integrale ∫ (sec x sin x) dx?
Qual es le resultado del integrale ∫ (sec x sin x) dx?
Signup and view all the answers
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?
Signup and view all the answers
Qual es le significato del simbolo ∫ in casa de calculus?
Qual es le significato del simbolo ∫ in casa de calculus?
Signup and view all the answers
Qual es le resultato del integrale ∫ (1/sin x cos x) dx?
Qual es le resultato del integrale ∫ (1/sin x cos x) dx?
Signup and view all the answers
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$?
Signup and view all the answers
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$?
Signup and view all the answers
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$?
Signup and view all the answers
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$?
Signup and view all the answers
Qual es le resultato del integral $
oot{2}{cot(x)} dx$?
Qual es le resultato del integral $ oot{2}{cot(x)} dx$?
Signup and view all the answers
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
-
Problem 12: Find the integral of x² tan⁻¹(x) / (1 + x²) dx
-
Problem 13: Calculate the definite integral of ∫ eˣ (x² + 1) / (x + 1)² dx (limits are not specified).
-
Problem 14: Calculate the integral of ∫ x / ((x² - a²) (x² - b²)) dx.
-
Problem 15: Evaluate the integral of (2x + 5) / √(x² + 2x + 5) dx.
-
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.
-
Problem 18: Find the value of ∫₀∞ (x² / ((x² + a²) (x² + b²) )) dx.
-
Problem 19: Given f(x) = {2x + 1, 1 ≤ x ≤ 2 / x² + 1, 2 ≤ x ≤ 3}, determine ∫₁³ f(x) dx.
-
Problem 20: Calculate the integral ∫ᵃᵇ cos x dx in terms of a and b using the limit approach.
-
Problem 21: Given f'(x) = 4x³ - (3 / x⁴) and f(2) = 0, find f(x).
-
Problem 22: Evaluate (x⁸ - 1)¹/³ x⁵ dx
-
Problem 23: Evaluate sin³ (2x + 1) dx.
-
Problem 24: Evaluate (cos 2x - cos 2a) / (cos x - cos a) dx.
-
Problem 25: Find the indefinite integral of (3x - 1) / ( (x - 1)(x - 2)(x - 3)) dx
-
Problem 26: Evaluate ∫₀π/2 log(4 + 3 sin x) / (4 + 3 cos x) dx
-
Problem 27: Given x² + 1 / x² + x³ = 1/x + 1/x² − 1/x³ (with details stated).
-
Problem 28: Evaluate √(x² + 1) [log(x² + 1) − 2 log x] / x⁴ dx.
-
Problem 29: Evaluate ∫ₙ /₆ sin x + cos x √(sin 2x) dx.
-
Problem 30: Calculate ∫₀¹ e⁻²⁻³ˣ dx using limit approach.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Related Documents
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.
