Question Solved1 Answer If the function f is continuous on the closed interval [a, b], then there exists at least one point c element of (a, b) such that  f (x)dx = f(c)(b – a).a Choose between sketch A or B to illustrate this theoremА.f(c)bf(c)В.'aC

ODGWBR The Asker · Calculus

If the function f is continuous on the closed interval [a, b], then there exists at least one point c element of (a, b) such that 

Transcribed Image Text: f (x)dx = f(c)(b – a).a Choose between sketch A or B to illustrate this theoremА.f(c)bf(c)В.'aC
More
Transcribed Image Text: f (x)dx = f(c)(b – a).a Choose between sketch A or B to illustrate this theoremА.f(c)bf(c)В.'aC
See Answer
Add Answer +20 Points
Community Answer
B38Z9O The First Answerer
See all the answers with 1 Unlock
Get 4 Free Unlocks by registration

Step 1given:the function f is continuous on the closed interval [a, b], then there exists at least one point c element of (a, b) such that ∫abf(x) dx=f(c)b-a we have to choose  between sketch A or B to illustrate the theorem. Step 2according to the given theorem we have∫abf(x) dx=f(c)b-a the value ∫abf(x) dx will give the area under the curve y=f(x) from x=a to x=b.the right hand side expression f(c)(b-a) is the area of the rectangle having length (b-a) and breadth equal to f(c).therefore point x=c should be selected such that the area under the curve from x=a to x=b is same as the single value of the function f(c) mutilplied by the length of the interval for which the area under the curve is calculated.  Step 3in sketch A the area under the curve ∫abf(x) ... See the full answer