Statics: Exam 2 Review Problem 5, Centroid by Calculus

Statics: Exam 2 Review Problem 5, Centroid by Calculus

Exam 2 is getting closer, and it’s time to tackle one of the most requested topics—Centroids by Calculus! In this video, we are solving Problem 4 from our Exam 2 Review series, focusing on how to find the Centroid (X-bar and Y-bar) of an area bounded by a parabolic curve and a straight line using integration.

No more relying on the back-of-the-book formula sheets! I will guide you step-by-step through the entire calculus process. First, we’ll use boundary conditions to find the constant ‘k’ and establish our equations. Then, I’ll show you how to set up a vertical differential strip to easily solve for X-bar.

But what about Y-bar? Instead of dealing with messy calculations, I’ll share my favorite trick—”Flip the Strip!” By switching to a horizontal strip, the math becomes incredibly clean, helping you avoid those costly exam-day mistakes. Grab your notebook, your calculator, and let’s master centroid integration together!

Key Highlights of this Lesson:

• Finding the constant ‘k’ and setting up parabolic and linear equations.

• Setting up the vertical differential strip ($dA$) for X-bar.

• The “Flip the Strip” trick: Switching to a horizontal strip for Y-bar.

• Complete step-by-step integration and boundary evaluation.

Timestamps:

00:12 – Setting up the Problem & Finding the Constant ‘k’

02:13 – Constructing the Linear Equation ($y=mx$)

02:54 – X-bar Calculation: Vertical Strip Setup & Integration

07:17 – Y-bar Calculation: Why We “Flip the Strip” (Horizontal Setup)

13:07 – Integrating for Y-bar & Final Answer Verification

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