Calculate Integrals

Calculate Indefinite Integrals

Example

Solve:

Integration using completing the square

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Example

Solve:

• Rewrite it to this form:

  
• Use the special arctan rule to solve it, and get:

  

Example

Solve: Solve:

• Rewrite it to this form:

  
• Use the special arctan rule to solve it, and get:

  

Calculate Definite Integrals

Example

Solve: Don't get confused when you see the Upper boundary is smaller than the Lower one.

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Example (piecewise integration)

Solve: The key is to seperate the intervals and integrate them piece by piece.

Example (Absolute value)

Solve:

• Splitting up the absolute value, and notice that the absolute value function is a piecewise function. Here we have that:

  
• Splitting up the definite integral:

  
• Evaluating each piece:

  

  
• Answer is 20.