What is the value of the integral ∫(1 to 2) (3x^2 - 2)dx?

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Question: What is the value of the integral ∫(1 to 2) (3x^2 - 2)dx?

Options:

Correct Answer: 4

Solution:

The integral evaluates to [x^3 - 2x] from 1 to 2 = (8 - 4) - (1 - 2) = 3.

What is the value of the integral ∫(1 to 2) (3x^2 - 2)dx?

What is the value of the integral ∫(1 to 2) (3x^2 - 2)dx?

Step 1: Identify the integral you need to solve: ∫(1 to 2) (3x^2 - 2)dx.
Step 2: Find the antiderivative of the function 3x^2 - 2. The antiderivative is x^3 - 2x.
Step 3: Evaluate the antiderivative at the upper limit (2): Substitute x = 2 into x^3 - 2x, which gives 2^3 - 2*2 = 8 - 4 = 4.
Step 4: Evaluate the antiderivative at the lower limit (1): Substitute x = 1 into x^3 - 2x, which gives 1^3 - 2*1 = 1 - 2 = -1.
Step 5: Subtract the value at the lower limit from the value at the upper limit: 4 - (-1) = 4 + 1 = 5.
Step 6: The final answer is 5.

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