1. Integration is a fundamental concept in calculus that involves finding the integral of a function. 2. The integral represents the area under the curve of a function over an interval. 3. There are two main types of integrals: indefinite integrals and definite integrals. 4. An indefinite integral, written as $$\int f(x) \, dx$$, represents a family of functions whose derivative is $$f(x)$$. It includes a constant of integration $$+ C$$. 5. A definite integral, written as $$\int_a^b f(x) \, dx$$, calculates the exact area under $$f(x)$$ from $$x=a$$ to $$x=b$$ and yields a number. 6. Basic integration rules include the power rule: $$\int x^n \, dx = \frac{x^{n+1}}{n+1} + C$$ for $$n \neq -1$$. 7. Integration techniques include substitution, integration by parts, partial fractions, and trigonometric integrals. 8. Example: Find $$\int x^2 \, dx$$. Step: Apply power rule with $$n=2$$. $$\int x^2 \, dx = \frac{x^{2+1}}{2+1}+C = \frac{x^3}{3}+C$$. 9. Example: Find $$\int_0^1 x^2 \, dx$$. Step: Use power rule, then evaluate definite integral. $$\int_0^1 x^2 \, dx = \left[ \frac{x^3}{3} \right]_0^1 = \frac{1^3}{3} - \frac{0^3}{3} = \frac{1}{3}$$. 10. Integration helps compute areas, volumes, displacement, and many quantities in physics, engineering, and beyond.