Podcast
Questions and Answers
ما هو التكامل الصحيح للدالة المثلثية ∫ sin 3x dx؟
ما هو التكامل الصحيح للدالة المثلثية ∫ sin 3x dx؟
- -3 cos 3x + c
- -1/6 cos 3x + c
- -3/2 cos 3x + c
- -1/3 cos 3x + c (correct)
كيف يتم التكامل للدالة ∫ csc² 5x dx؟
كيف يتم التكامل للدالة ∫ csc² 5x dx؟
- -5 cot 5x + c
- 1/5 cot 5x + c
- 5 cot 5x + c
- -1/5 cot 5x + c (correct)
ما هو الناتج الصحيح للتكامل ∫ sec 4x tan 4x dx؟
ما هو الناتج الصحيح للتكامل ∫ sec 4x tan 4x dx؟
- 1/4 sec 4x + c (correct)
- 4 sec 4x + c
- 1/2 sec 4x + c
- 1 sec 4x + c
ما هو التكامل الصحيح للدالة ∫ cos 6x dx؟
ما هو التكامل الصحيح للدالة ∫ cos 6x dx؟
Flashcards
تكامل sin ax
تكامل sin ax
تكامل sin ax يساوي -1/a cos ax + c
تكامل cos ax
تكامل cos ax
تكامل cos ax يساوي 1/a sin ax + c
تكامل sec² ax
تكامل sec² ax
تكامل sec² ax يساوي 1/a tan ax + c
تكامل csc² ax
تكامل csc² ax
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تكامل sec ax tan ax
تكامل sec ax tan ax
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Study Notes
Calculus Study Notes
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Integration is the reverse process of differentiation.
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The symbol ∫ represents integration.
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dx indicates integration with respect to x; dy indicates integration with respect to y.
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There's no general rule for integrating fractions, roots, or products of functions.
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Indefinite Integrals:
- The integral of a constant 'a' with respect to x is ax + c, where 'c' is the constant of integration.
- The integral of xn with respect to x is (xn+1) / (n + 1) + c.
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Examples of Indefinite Integrals:
- ∫ 6 dx = 6x + c
- ∫ √5 dx = √5x + c
- ∫x2dx = (x3) / 3 + c
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Definite Integrals: The definite integral of a function f(x) from a to b is evaluated as [F(x)]ab = F(b) - F(a), where F(x) is the antiderivative of f(x). No constant of integration 'c' is added.
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Properties of Integrals:
- The integral of a constant multiple of a function is the constant multiple of the integral of the function.
- The integral of a sum or difference of functions is the sum or difference of their individual integrals.
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Rules for integrating functions with exponents.
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Rules for integrating functions with radicals.
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Rules for integrating polynomial functions.
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Integration rules and properties for different types of functions (e.g., exponential, trigonometric, logarithmic, and hyperbolic).
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