Find the value of the definite integral ∫(1 to 4) (x^3) dx. (2019)

Find the value of the definite integral ∫(1 to 4) (x^3) dx. (2019)

Step 1: Identify the integral you need to solve: ∫(1 to 4) (x^3) dx.
Step 2: Find the antiderivative of x^3. The antiderivative is (x^4)/4.
Step 3: Write the expression for the definite integral using the antiderivative: [(x^4)/4] from 1 to 4.
Step 4: Substitute the upper limit (4) into the antiderivative: (4^4)/4 = (256)/4 = 64.
Step 5: Substitute the lower limit (1) into the antiderivative: (1^4)/4 = (1)/4 = 0.25.
Step 6: Calculate the definite integral by subtracting the lower limit result from the upper limit result: 64 - 0.25 = 63.75.
Step 7: Since the answer is usually expressed as a fraction, convert 0.25 to 1/4 and perform the subtraction: 64 - 1/4 = 63.75.

Definite Integral – The process of calculating the area under a curve defined by a function over a specific interval.
Fundamental Theorem of Calculus – This theorem connects differentiation and integration, allowing the evaluation of definite integrals using antiderivatives.
Polynomial Integration – The technique of integrating polynomial functions, which involves applying the power rule for integration.