Basic Integration Formulas for Calculus 1  Summary and Q&A
TL;DR
This video explains three basic integration rules: the formula for integrating zero, the formula for integrating a constant, and the power rule.
Key Insights
 The integral of zero with respect to X is the constant function.
 ✖️ Integrating a constant with respect to X results in the constant multiplied by X, plus a constant of integration.
 ✊ The power rule is a fundamental rule for integration, allowing us to integrate functions of the form X to the power of n.
 🍉 The sum rule enables us to integrate functions by integrating each term separately.
 ❓ Integration is the process of finding the antiderivative of a function.
 ❓ The constant of integration can take any value and represents the many possible solutions to an indefinite integral.
 ✊ The power rule is only valid for exponents that are not equal to 1.
Transcript
hi everyone in this video we're going to discuss some of the basic integration rules so the first rule we're going to look at is a formula for the integral of zero with respect to X so when we're trying to integrate zero with respect to X we have to ask ourselves what is a function whose derivative is zero right because we're going backwards well t... Read More
Questions & Answers
Q: What is the formula for integrating zero with respect to X?
The formula states that the integral of zero with respect to X is the constant function. This is because the derivative of a constant function is zero, and integrating zero should bring us back to the constant function.
Q: How do we integrate a constant with respect to X?
To integrate a constant, denoted as K, with respect to X, we simply multiply the constant by X and add a constant of integration. This is because the derivative of KX is K, and the derivative of a constant is zero.
Q: What is the power rule for integration?
The power rule states that when integrating X to the power of n with respect to X, we add 1 to the exponent, divide by the new exponent, and add a constant of integration. This formula is valid as long as the exponent is not equal to 1.
Q: How do we integrate the function 2x + 3 with respect to X?
We can integrate each term separately using the sum rule. For the term 2x, we apply the power rule to get (2/2)x^2 = x^2, and for the term 3, we simply multiply by X to get 3x. The result is x^2 + 3x + C, where C is the constant of integration.
Summary & Key Takeaways

The first integration rule states that when integrating zero with respect to X, the result is the constant function.

The second integration rule states that when integrating a constant with respect to X, the result is the constant multiplied by X, plus a constant of integration.

The third integration rule, known as the power rule, states that when integrating X to the power of n with respect to X, the result is X to the power of n+1 divided by n+1, plus a constant of integration.