Evaluate the following Integral: ∫f(x)dx, x ∈ [0, 9], where f(x) = {(sin x, 0 ≤ x ≤ π/2), (1, π/2 ≤ x ≤ 3 ), e^(x -3, 3 ≤ x ≤ 9 )

Question

Evaluate the following Integral:

\(\int\limits_{0}^{9} \)f(x) dx, where f(x) = \( \begin{cases} sin\,\text x, & \quad 0\leq\text x\leq\pi/2\\ 1, & \quad \pi/2\leq\text x\leq3\\ e^{\text x-3},&\quad 3\leq\text x\leq9 \end{cases} \)

Answer 1

We have, \(\int\limits_0^9\)f(x)dx