∫ calculus

1. **State the problem:** We need to evaluate the integral $$\int -21(-x^2 - x + 2) \, dx$$. 2. **Rewrite the integral:** Distribute the constant $$-21$$ inside the integral:

1. **State the problem.** We want to evaluate the integral $\int_{-2}^3 f(x^3-2x^2-5x+6)\,dx$.

1. **State the problem:** We need to find the derivative $f'(x)$ of the function $$f(x) = (3x^2 + 1)\sqrt{5 + x}.$$ 2. **Rewrite the function:** Note that $$\sqrt{5 + x} = (5 + x)^

1. **State the problem:** Find the derivative of the function $$f(x) = (3x^2 + 1)\sqrt{5} + x$$. 2. **Recall the rules:**

**Area of a Triangle and Introduction to Integration** 1. **Area of a Right Triangle**

### **Area of a Right Triangle** 1. **Problem Statement:** Calculate the area of a right triangle with base and height both equal to 4 units.

**Integral Evaluation of $(3 - 4x)^3$ from $-1$ to $2$** **1. Problem Statement**

**Evaluating the Definite Integral Using Substitution** **1. Problem Statement**

**Integration of Power Functions** **1. Understanding the basic integral formula**

**Integral of $ax^n$** 1. **Understanding the integral formula**

**Integration of Power Functions** **1. Understanding the integral of $a x^n$**

**Integration of Polynomial and Fractional Functions** **Problem Overview**

**Integration of Polynomial and Fractional Expressions** **Part A: Integration of Polynomial Expression**

**Integration of Polynomial and Fractional Functions** **Problem Statement**

**Integral Calculus and Area Under a Curve** **1. Problem Statement**

1. **State the problem:** Find the derivative of the function $f(x) = x^3 + 2x$. 2. **Recall the derivative rules:**

1. **State the problem:** Evaluate the integral $$\int \frac{7x^{2} + 8x - 4}{(x + 1)(x^{2} + x - 1)} \, dx$$.

1. **State the problem:** Find \( \lim_{x \to 3} \frac{x^2 - 9}{x - 3} \).

1. لنبدأ بمسألة حقيقية: حساب التكامل غير المحدد للدالة $f(x) = 3x^2 + 2x + 1$. 2. صيغة التكامل الأساسية هي $\int f(x) \, dx$ حيث $f(x)$ هي الدالة التي نريد تكاملها.

1. لنبدأ بتعريف المشكلة: نريد حساب التكامل المحدد أو غير المحدد لدالة معينة. 2. صيغة التكامل الأساسية هي $$\int f(x) \, dx$$ حيث $f(x)$ هي الدالة التي نريد تكاملها.

1. **Problem statement:** Given the function $f(x) = 0.5x^2 - 3x - 1$, find the equation of the tangent line to the graph $G_f$ that is parallel to the given line $g$. We will solv