Question

Evaluate the integral ∫(10x² + 49) dx. (Remember to use absolute values where appropriate. Use C for the constant of integration.)

Answer 1

To evaluate the integral ∫(10x² + 49) dx, we can use the power rule of integration. The evaluated integral is (10/3)x^3 + 49x + C.

Step-by-step explanation:

To evaluate the integral ∫(10x² + 49) dx, we can use the power rule of integration. The power rule states that the integral of x^n is (1/(n+1))x^(n+1), where n is any real number except -1. Applying this rule to the integral, we can rewrite it as ∫10x² dx + ∫49 dx. The integral of 10x² dx can be evaluated as (10/3)x^3 + C, where C is the constant of integration. The integral of 49 dx is simply 49x + C. Therefore, the evaluated integral is (10/3)x^3 + 49x + C.