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Introduction to Integrals

Math
Summary

Problems for "The Definite Integral" 3

Summary Problems for "The Definite Integral" 3

Problem : Evaluate: sin(x)dx.

-cos(x)0Π=-(-1)-(-1) = 2    

Problem : Evaluate: (x2-5x)dx.

(x3 - x2)01=( - ) - (0) =    

Problem : Evaluate: (4x2+1)dx.

x3 + x-10=(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