(9) Assume that functions f and g are continuous for all x. Find the values of theindicated integrals from the given data. (5.2)n onbogenibeauFind S, 3 f(x) dx if S(f(x) – g(x)) dx = 3 and S, g(x) dx = –1.a.b. Find S g(x) dx if g(x) dx = 3 and S, 2 g(x) dx = 8.c. Find g(x) dx if g(x) dx = 4, f 2. g(x) dx = 6 , and S, g(x) dx = 5.

Name: (9) Assume that functions f and g are continuous for all x. Find the
Uploaded: 2024-03-20T07:06:41.000Z
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Description: (9) Assume that functions f and g are continuous for all x. Find the values of theindicated integrals from the given data. (5.2)n onbogenibeauFind S, 3 f(x) dx if S(f(x) – g(x)) dx = 3 and S, g(x) dx = –1.a.b. Find S g(x) dx if g(x) dx = 3 and S, 2

Properties of definite integral: a. We need to find ∫013.f(x) dxWhere ∫01(f(x)-g(x))dx=3and ∫01g(x) dx=-1∫01(f(x)-g(x))dx=∫01f(x)dx-∫01g(x)dx 3=∫01f(x)dx-(-1) 3-1=∫01f(x)dx ∫01f(x)dx=2Therefore ,∫013.f(x)dx=3.∫01f(x)dx =3.2 =6b.∫01g(x)dx=∫02g(x)dx+∫21g(x)dxAgain,∫122.g(x)dx=-2∫21g(x)dx 8=-2.∫21g(x)dx -4=∫21g(x)dxTherefore ∫01g(x)dx=∫02g(x)dx+∫21g(x)dx =3-4=-1c.∫25g(x)dx=∫28g(x)dx+∫81g(s)dx+∫15g(x)dx-∫81g(x)dx=∫18g(x)dx-4=∫81g(x)dx∫15g(x)dx=-∫51g(x)dx =-62=-3∫25g(x)dx=∫28g(x)dx+∫81g(s)dx+∫15g(x)dx =5-4-3=-2