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

₹0.0

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

Options:

Correct Answer: 1

Solution:

The integral evaluates to [x^3] from 0 to 1 = 1^3 - 0^3 = 1.

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

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

Step 1: Identify the integral you need to solve, which is ∫(0 to 1) (3x^2)dx.
Step 2: Find the antiderivative of the function 3x^2. The antiderivative is x^3 (because the integral of x^n is (x^(n+1))/(n+1)).
Step 3: Write the antiderivative with the limits of integration: [x^3] from 0 to 1.
Step 4: Evaluate the antiderivative at the upper limit (1): 1^3 = 1.
Step 5: Evaluate the antiderivative at the lower limit (0): 0^3 = 0.
Step 6: Subtract the lower limit result from the upper limit result: 1 - 0 = 1.
Step 7: Conclude that the value of the integral is 1.

No concepts available.