Answer:
Therefore, the value of the definite integral ∫[a to b] (11 + 9x²)dx is 11b + 3b^3 - 11a - 3a^3.
Explanation:
1. Apply the power rule for integration:
Using the power rule, we can integrate each term separately. The integral of a constant is the constant multiplied by the variable, and the integral of x^n is (x^(n+1))/(n+1).
∫[a to b] (11 + 9x²)dx = [11x + (9/3)x^3] [a to b]
2. Evaluate the integral limits:
Substituting the upper limit (b) and the lower limit (a) into the integral expression:
[(11b + (9/3)b^3)] - [(11a + (9/3)a^3)]
3. Simplify the expression:
Simplify the terms and calculate the result:
(11b + 3b^3) - (11a + 3a^3)
11b + 3b^3 - 11a - 3a^3
Therefore, the value of the definite integral ∫[a to b] (11 + 9x²)dx is 11b + 3b^3 - 11a - 3a^3.