find the area bounded by the curves y=sinx, y=3x, and y=30-3x?

Answer 1

the lower boundary is sin(x) ...

the upper boundaries are 3x first... then 30-3x next... cut it at x=5.

thus

area =
∫ [0,5] {3x - sinx} dx + ∫ [5,10] {30-3x-sinx} dx

solve...


§

Answer 2

y = sinx
y = 3x
y = 30 - 3x
6x = 30
x1 = 5
x2 ≈ 10.243402184859
A =
5
∫(3x - sin(x)
0
+
10.2434
∫(30 - 3x - sin(x)
5
A ≈ (3/2)(25) + cos(5) - 1 + (30)(10.2434 - 5) - (3/2)(10.2434)^2 + (3/2)(25) + cos(10.2434) - cos(5)
A ≈ (3)(25) - 1 + (30)(5.2434) - (3/2)(10.2434)^2 + cos(10.2434)
A ≈ 74 + 157.3021 - 157.3909 + 0.9841
A ≈ 74.895