Evaluate ∫ from 0 to 1 of (x^4) dx.

Evaluate ∫ from 0 to 1 of (x^4) dx.

Correct Answer: 1/5

Step 1: Identify the integral you need to evaluate, which is ∫ from 0 to 1 of (x^4) dx.
Step 2: Find the antiderivative of x^4. The antiderivative is (x^(4+1))/(4+1) = x^5/5.
Step 3: Write down the antiderivative: (x^5)/5.
Step 4: Evaluate the antiderivative at the upper limit (1): (1^5)/5 = 1/5.
Step 5: Evaluate the antiderivative at the lower limit (0): (0^5)/5 = 0.
Step 6: Subtract the lower limit result from the upper limit result: (1/5) - (0) = 1/5.
Step 7: Conclude that the value of the integral is 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 functions of the form x^n, where the integral is (x^(n+1))/(n+1) + C.