Evaluate ∫ from 0 to 1 of (x^3 + 3x^2 + 3x + 1) dx.
Practice Questions
1 question
Q1
Evaluate ∫ from 0 to 1 of (x^3 + 3x^2 + 3x + 1) dx.
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The integral evaluates to [x^4/4 + x^3 + (3/2)x^2 + x] from 0 to 1 = (1/4 + 1 + 3/2 + 1) = 4.
Questions & Step-by-step Solutions
1 item
Q
Q: Evaluate ∫ from 0 to 1 of (x^3 + 3x^2 + 3x + 1) dx.
Solution: The integral evaluates to [x^4/4 + x^3 + (3/2)x^2 + x] from 0 to 1 = (1/4 + 1 + 3/2 + 1) = 4.
Steps: 6
Step 1: Identify the integral you need to evaluate: ∫ from 0 to 1 of (x^3 + 3x^2 + 3x + 1) dx.
Step 2: Find the antiderivative of the function (x^3 + 3x^2 + 3x + 1).
Step 3: The antiderivative is calculated as follows: For x^3, the antiderivative is (x^4)/4; for 3x^2, it is 3(x^3)/3 = x^3; for 3x, it is (3/2)x^2; and for 1, it is x.
