Step 1: Identify the integral you need to solve: ∫_0^π sin(x) dx.
Step 2: Find the antiderivative of sin(x). The antiderivative is -cos(x).
Step 3: Evaluate the antiderivative at the upper limit (π): -cos(π) = -(-1) = 1.
Step 4: Evaluate the antiderivative at the lower limit (0): -cos(0) = -1.
Step 5: Subtract the lower limit result from the upper limit result: 1 - (-1) = 1 + 1 = 2.
Step 6: Conclude that the value of the integral ∫_0^π sin(x) dx is 2.
Definite Integral – The question tests the understanding of evaluating definite integrals, specifically the integral of the sine function over a specified interval.
Fundamental Theorem of Calculus – It assesses the application of the Fundamental Theorem of Calculus, which connects differentiation and integration.
Trigonometric Functions – The question involves knowledge of trigonometric functions, particularly the sine function and its properties.
