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Problems for "The Definite Integral"

Problems for "The Definite Integral"

Problems for "The Definite Integral"

Problems for "The Definite Integral"

Problems for "The Definite Integral"

Problems for "The Definite Integral"

Problem : Evaluate: sin(x)dx .

-cos(x) 0 Π =-(-1)-(-1) = 2    

Problem : Evaluate: (x 2-5x)dx .

( x 3 - x 2) 0 1=( - ) - (0) =    

Problem : Evaluate: (4x 2+1)dx .

x 3 + x -1 0=(0) - ( -1) =    

Problem : What is the relationship between f (x)dx and f (x)dx?

Since


f (x)dx   = F(b) - F(a), and  
f (x)dx   = F(a) - F(b),  
f (x)dx   = - f (x)dx  

Problem : For the function graphed below, find


    f (x)dx  
    f (x)dx  
    f (x)dx  

Recall the interpretation of the definite integral as the signed area under the curve. Portions below the graph count as "negative area" even though such a thing could not exist geometrically.


f (x)dx   = 3 - 1 + 2 = 4  
f (x)dx   = 1  
f (x)dx   = 3 - 1 + 2 - 5 = - 1