The integral evaluates to [x^3/3 + 2x^2 + 4x] from 0 to 1 = (1/3 + 2 + 4) = 25/3.
Questions & Step-by-step Solutions
1 item
Q
Q: Calculate ∫ from 0 to 1 of (x^2 + 4x + 4) dx.
Solution: The integral evaluates to [x^3/3 + 2x^2 + 4x] from 0 to 1 = (1/3 + 2 + 4) = 25/3.
Steps: 8
Step 1: Identify the function to integrate, which is (x^2 + 4x + 4).
Step 2: Find the antiderivative of the function. The antiderivative of x^2 is x^3/3, the antiderivative of 4x is 2x^2, and the antiderivative of 4 is 4x.
Step 3: Combine the antiderivatives to get the complete antiderivative: (x^3/3 + 2x^2 + 4x).
Step 4: Evaluate the antiderivative from the lower limit (0) to the upper limit (1).
Step 5: Substitute 1 into the antiderivative: (1^3/3 + 2*1^2 + 4*1) = (1/3 + 2 + 4).
