Integral Calculus Notes and Examples

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Questions and Answers

𝑓(𝑥) = ∫2𝑒^𝑡+1𝑑𝑡 ise, 𝑓′(1) kaçtır?

2
3 (correct)
5
4

Örnek 3 için 𝐴 + 𝐵 = 6 olduğuna göre, 𝐵 kaçtır?

6
5
4
3 (correct)

𝑓(𝑥) = ∫5∫π/2 𝑥−4𝑑𝑥 integralinin değeri nedir?

-3
-4
4 (correct)
3

Bir fonksiyonun diferansiyeli ne demektir?

f '(x).x ifadesi (C) Signup and view all the answers

Belirsiz integral nedir?

F(x) + c ifadesine denir (C) Signup and view all the answers

Hangisi belirsiz integralin kurallarından biri değildir?

∫f(x) dx = F(x) + c (B) Signup and view all the answers

F(x) = 2.( x^3 + 2).3x^2 olarak tanımlanan fonksiyon için F(0) kaçtır?

0 (C) Signup and view all the answers

Verilen integralin sonucu hangisidir: ∫x^2 dx?

$\frac{1}{4}x^4 + C$ (D) Signup and view all the answers

Eğer F(-1) = ln2 ise, F(0) kaçtır?

$ln(\frac{1}{2})$ (B) Signup and view all the answers

Verilen integral hangi ifadeyle eşdeğerdir: ∫(x^3 - x^2) dx?

$\frac{1}{4}x^4 - \frac{1}{3}x^3 + C$ (B) Signup and view all the answers

Flashcards

Derivative of a function

The derivative of 𝑓(𝑥) with respect to 𝑥, denoted as 𝑓′(𝑥), represents the instantaneous rate of change of 𝑓(𝑥) at a specific value of 𝑥. It essentially describes how the value of 𝑓(𝑥) changes as 𝑥 changes infinitesimally.

Continuity in Calculus

A function is continuous at a point if its graph can be drawn without lifting the pen, and its limit at that point exists and equals the function's value at that point.

Derivative in context

The derivative of a function is the rate at which the function's output changes with respect to its input. It can also be interpreted as the slope of the tangent line to the function's graph at a specific point.

What is Derivative?

The derivative of a function measures the instantaneous rate of change of the function's output with respect to its input. It represents the slope of the tangent line to the graph of the function at a specific point.