Final answer:
To evaluate the integral of (15x²-3x+8)dx, apply the power rule for integration. Substituting the given value, solve for the constant C.
Step-by-step explanation:
To evaluate the integral of (15x²-3x+8)dx, we can use the power rule for 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 the power rule, we get:
(15/3)x^3 - (3/2)x^2 + 8x + C
We are given that when x=3, the value of the integral is 30. Substituting x=3 into the expression, we can solve for the constant C:
(15/3)(3^3) - (3/2)(3^2) + 8(3) + C = 30
Simplifying, we get: 135 - 13.5 + 24 + C = 30
Combining like terms, we have: 145.5 + C = 30
Finally, subtracting 145.5 from both sides gives us: C = -115.5.
Therefore, the value of the integral is:
(15/3)x^3 - (3/2)x^2 + 8x - 115.5