Definite integration.pdf

The fundamental theorem of calculus relates definite integration to...

The fundamental theorem of calculus relates definite integration to differentiation. Fundamental theorem of calculus It states that if a function is continuous on a closed interval and has an antiderivative, then the definite integral of the function over the interval is equal to the difference of the antiderivative evaluated at the endpoints of the interval. Substitution method: Involves replacing a variable with a new variable to simplify the integral. Integration by parts: Involves integrating the product of two functions using a specific formula. Techniques for evaluating definite integrals Trigonometric substitution: Involves replacing the variable with a trigonometric function to simplify the integral. Partial fractions: Involves decomposing a rational function into simpler fractions combinedintervalisequaltothesumofintegralsoverindivi and then integrating each term separately. Definite integration dualintervals Area under a curve: Definite integration can be used to find the area between a curve and the x-axis over a specific interval. Calculating displacement: Definite integration can be used to calculate the Applications of definite integration displacement of an object when its velocity is known. Finding average values: Definite integration can be used to calculate the average value of a function over a specific interval. Improper integrals: Involves integrating over unbounded intervals or functions with infinite discontinuities. Numerical methods: Techniques such as numerical approximation and numerical integration can be used to estimate definite integrals. Advanced topics in definite integration Multivariable integration: Definite integration can be extended to integrate functions of multiple variables over a region in space. Applications in physics and engineering: Definite integration has various applications in solving problems related to physics, engineering, and other scientific fields.