I integrated the quadratic formula

TL;DR

Learn how to integrate the quadratic formula with respect to the variable a.

Transcript

okay as we all know this right here is the  quadratic formula and I'm pretty sure you   have seen it before but have you ever tried  to integrate this I don't think so in fact we   differentiated this last year already if you  haven't seen that video the link is in the   description today let's integrate this and last  year we did it with respect t... Read More

Key Insights

• 🎭 Integrating the quadratic formula involves splitting the fractions and performing separate integrations.
• 💦 A substitution method can be used by letting U equal the square root part of the quadratic formula.
• 🍉 The integral of U^2/(4C) can be simplified by canceling out the common terms in the numerator and denominator.

Questions & Answers

Q: How do you split the fractions and integrate B/(2a) and 1/a?

To split the fractions, separate the terms B/(2a) and 1/a. For B/(2a), the integral will be negative B/(2a). For 1/a, integrate as the natural logarithm of the absolute value of a.

Q: What substitution method is used in the second part?

In the second part, a substitution method is used by letting U equal the square root part of the quadratic formula. This is done to simplify the integration process.

Q: How can the integral of U^2/(4C) be simplified?

The integral of U^2/(4C) can be simplified by canceling out the 4C terms in the numerator and denominator. The result is just the integral of U^2.

Q: What is the formula for integrating 1/(u^2 - b^2) in the U world?

The formula for integrating 1/(u^2 - b^2) in the U world is the inverse hyperbolic tangent. The integral is -1/b times the inverse hyperbolic tangent of (U/b).

Summary & Key Takeaways

• The video tutorial demonstrates the process of integrating the quadratic formula with respect to the variable a.

• The first part of the integration involves splitting the fractions and integrating B/(2a) and 1/a.

• In the second part, a substitution method is used, letting U equal the square root part of the quadratic formula.