Determine the area of the indicated region accurate to three decimal places:

y=x+sinx [0,π]

Area = ∫ y dx
In this scenario:
Area = ∫ x + sin(x) dx between limits 0 and pi
Area = (x^2)/2 - cos(x) between limits 0 and pi
Area = [((pi)^2)/2 - cos(pi)] - [(0^2)/2 - cos(0)]
Area = [((pi)^2)/2 - (-1)] - [0 - 1]
Area = ((pi)^2)/2 + 1 + 1
Area = 4.9348 + 2
Area = 6.935 (to three decimal places)

A = ∫ [0 to π] (x + sinx) dx
A = (x²/2 − cosx) | [0 to π]
A = (π²/2 − cos(π)) − (0 − cos(0))
A = π²/2 − (−1) − 0 + 1
A = π²/2 + 2

A ≈ 6.934802201 = 6.935 (to 3 decimal places)

Area = integral y dx

= [(x^2/2) - cosx ] = pi^2 / 2 +1 +1 = 6.935 units^2