V = π∫ 10(y − y4) dy = 3π/10

To solve the given equation, we need to find the value of V by evaluating the integral.

Step 1: Identify the limits of integration. In this case, the limits are not explicitly given, so we need to determine them from the given equation. Since the integral is with respect to y, we can assume that the limits are the values of y that make the expression inside the integral equal to zero.

Step 2: Set up the integral. The given equation is V = π∫ 10(y − y^4) dy.

Step 3: Simplify the expression inside the integral. Distribute the 10 to both terms inside the parentheses: V = π∫ 10y - 10y^4 dy.

Step 4: Evaluate the integral. Integrating each term separately, we get V = π(5y^2 - 2y^5) + C, where C is the constant of integration.

Step 5: Apply the limits of integration. Since the limits were not given, we cannot determine the exact value of V. However, we can use the given information that V = 3π/10 to solve for the constant of integration C.

Step 6: Substitute the value of V and solve for C. 3π/10 = π(5y^2 - 2y^5) + C. Rearranging the equation, we get C = 3π/10 - π(5y^2 - 2y^5).

Step 7: Simplify the expression for C. C = 3π/10 - 5πy^2 + 2πy^5.

Therefore, the final equation is V = π(5y^2 - 2y^5) + 3π/10.