Evaluate ∫_0^1 (x^4) dx.

Evaluate ∫_0^1 (x^4) dx.

Step 1: Identify the integral to evaluate, which is ∫_0^1 (x^4) dx.
Step 2: Find the antiderivative of x^4. The antiderivative is (x^5)/5.
Step 3: Write the expression for the definite integral using the antiderivative: [(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 definite integral 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 over a specified interval.
Power Rule for Integration – A method for integrating polynomial functions, where ∫x^n dx = (x^(n+1))/(n+1) + C.