Volumes of Revolution – Washer Method Steps for volumes of revolution between two curves (Washer Method): 1. 2. 3. 4. Identify points of intersection if they are not given. These will be your limits of integration Graph (Sketch) both functions Identify which function is greater on the interval. 𝑏 If f(x) > g(x), The volume of the solid formed is ∫𝑎 𝜋[𝑓(𝑥)]2 − [𝑔(𝑥)]2 . Substitute the functions and limits of integration into this formula 5. Anti-differentiate and solve 1. Find the volume of the solid of revolution generated by revolving the region bounded by f(x)= x2 and g(x) = 4 about the x–axis. Step 1: Find points of intersection Step 2: Sketch curves Step 3: Which function is greater on the interval? Step 4: Substitute the functions into the 𝑏 formula: 𝜋 ∫𝑎 [𝑓(𝑥)]2 − [𝑔(𝑥)]2 Step 5: Anti-Differentiate and solve. Volumes of Revolution – Washer Method 2. Find the volume of the solid of revolution generated by revolving the region bounded by y = x2 and y = 4x – x2 about the x–axis 3. Find the volume of the solid of revolution generated by revolving the region bounded by y = 6 – 2x – x2 and y = x + 6 about the x–axis 4. Find the volume of the solid of revolution generated by revolving the region bounded by f(x) = sin x, g(x) = cos x, 0 < x < /4