The graph of g consists of two straight lines and a semicircle. Use it to evaluate each integral.

Question

Link to graph: https://ibb.co/zJ81nn1

find:

(a)    10	g(x) dx
0

(b)    30	g(x) dx
10

(c)    35	g(x) dx
0

Answer 1

Just remember that the area above the x-axis is positive, and the one below is negative.

∫¹⁰₀ g(x) dx is the area of a triangle = (1/2)bh:

∫¹⁰₀ g(x) dx = (1/2)(10)(20) =100 sq. units

∫³⁰₁₀ g(x) dx is a semi-circle but below the x-axis = -(1/2)πr²:

∫³⁰₁₀ g(x) dx = -(1/2)π(10)² = -50π sq. units

∫³⁵₀ g(x) dx = 100 - 50π + (1/2)(5)(5) = 112.5 - 50π ≈ -44.58 sq. unit