Definite and Indefinite Integral Practice

1. Do the following integrals
   

   $$\int \left( \frac{1}{x} + \frac{1}{x^2} \right) \, dx$$ (1)

   
   

   
   

   $$\int \pi x^3 \, dx$$ (2)

   
   

   
   

   $$\int ( 2 \cos x - 5 \sin x ) \, dx$$ (3)

   
   

   
   

   $$\int_0^5 \frac{x^3}{5} \, dx \\$$ (4)

   
   

2. Do the following integral. Express your answer both symbolically and numerically.
   

   $$\int_2^3 \frac{1}{2x} \\$$ (5)

   
   

3. Without actually doing the two integrals, which of the following is larger?

   
   

   $$\int_0^1 x^2 \, dx$$ (6)

   
   

   
   

   $$\int_0^1 x^3 \, dx \\$$ (7)

   
   

4. Evaluate the two integrals above and confirm your suspicions.