The integral evaluates to [x^2 + x] from 1 to 3 = (9 + 3) - (1 + 1) = 10.
Questions & Step-by-step Solutions
1 item
Q
Q: Evaluate ∫_1^3 (2x + 1) dx.
Solution: The integral evaluates to [x^2 + x] from 1 to 3 = (9 + 3) - (1 + 1) = 10.
Steps: 6
Step 1: Identify the function to integrate, which is (2x + 1).
Step 2: Find the antiderivative of the function. The antiderivative of 2x is x^2, and the antiderivative of 1 is x. So, the antiderivative of (2x + 1) is x^2 + x.
Step 3: Write the definite integral using the antiderivative. We need to evaluate [x^2 + x] from 1 to 3.
Step 4: Substitute the upper limit (3) into the antiderivative: (3^2 + 3) = (9 + 3) = 12.
Step 5: Substitute the lower limit (1) into the antiderivative: (1^2 + 1) = (1 + 1) = 2.
Step 6: Subtract the result of the lower limit from the result of the upper limit: 12 - 2 = 10.
