What is the value of the integral ∫(0 to 1) (3x^2 + 2)dx?

₹0.0

Question: What is the value of the integral ∫(0 to 1) (3x^2 + 2)dx?

Options:

Correct Answer: 5/3

Solution:

Integral = [x^3 + 2x] from 0 to 1 = (1 + 2) - (0) = 3.

What is the value of the integral ∫(0 to 1) (3x^2 + 2)dx?

What is the value of the integral ∫(0 to 1) (3x^2 + 2)dx?

Step 1: Identify the integral you need to solve: ∫(0 to 1) (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 (1): (1^3 + 2*1) = (1 + 2) = 3.
Step 4: Evaluate the antiderivative at the lower limit (0): (0^3 + 2*0) = (0 + 0) = 0.
Step 5: Subtract the value at the lower limit from the value at the upper limit: 3 - 0 = 3.
Step 6: The value of the integral is 3.

No concepts available.