Evaluate the integral
\[
\int_{0}^{\pi}(6 \sin (t)-9 \cos (t)) d t
\]

Integral =

Answer

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Answer

Final Answer: \(\boxed{12}\)

Steps

Step 1 ：Given the integral \(\int_{0}^{\pi}(6 \sin (t)-9 \cos (t)) d t\)

Step 2 ：First, we need to integrate the function \(6 \sin (t)-9 \cos (t)\) with respect to \(t\)

Step 3 ：The integral of \(\sin(t)\) is \(-\cos(t)\) and the integral of \(\cos(t)\) is \(\sin(t)\)

Step 4 ：Substitute the limits of integration \(\pi\) and \(0\) into the antiderivative

Step 5 ：Subtract the two results to get the final answer

Step 6 ：The result of the integral calculation is 12

Step 7 ：Final Answer: \(\boxed{12}\)