Final answer:
To evaluate the integral ∫(x² - 49 - x²) dx, simplify the expression inside the integral then perform the integration. The final answer is -49x + c, where c is the constant of integration.
Step-by-step explanation:
To evaluate the integral ∫(x² - 49 - x²) dx, we can simplify the expression inside the integral first. Notice that x² - x² is equal to zero, so we are left with ∫(-49) dx. Since -49 is a constant, we can pull it out of the integral:
∫(-49) dx = -49 ∫dx
The integral of dx is simply x, so the final answer is -49x + c, where c is the constant of integration.