Evaluate the following definite integral:∫𝜋30sin(𝑥) d𝑥

Sure, here are the steps to evaluate the definite integral:

1. Identify the integral: ∫sin(x) dx from π/3 to π.

2. Find the antiderivative of sin(x), which is -cos(x).

3. Apply the Fundamental Theorem of Calculus, which states that the definite integral of a function from a to b is F(b) - F(a), where F is the antiderivative of the function.

4. Substitute π and π/3 into -cos(x):

   F(π) = -cos(π) = -(-1) = 1 F(π/3) = -cos(π/3) = -1/2

5. Subtract F(π/3) from F(π) to get the result:

   1 - (-1/2) = 1 + 1/2 = 1.5 or 3/2.