Find the value of ∫ from 0 to 1 of (x^4) dx.

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Question: Find the value of ∫ from 0 to 1 of (x^4) dx.

Options:

Correct Answer: 1/5

Solution:

The integral evaluates to [x^5/5] from 0 to 1 = 1/5.

Find the value of ∫ from 0 to 1 of (x^4) dx.

Find the value of ∫ from 0 to 1 of (x^4) dx.

Step 1: Identify the integral you need to solve, which is ∫ from 0 to 1 of (x^4) dx.
Step 2: Find the antiderivative of x^4. The antiderivative is (x^5)/5.
Step 3: Write down the antiderivative with limits: [(x^5)/5] from 0 to 1.
Step 4: Substitute the upper limit (1) into the antiderivative: (1^5)/5 = 1/5.
Step 5: Substitute the lower limit (0) into the antiderivative: (0^5)/5 = 0.
Step 6: Calculate the final result by subtracting the lower limit result from the upper limit result: (1/5) - (0) = 1/5.

Definite Integral – The process of calculating the area under the curve of a function between two specified limits.
Power Rule for Integration – A method for integrating polynomial functions, where ∫x^n dx = (x^(n+1))/(n+1) + C.