Evaluate each of the following integrals.

Question

       2

1)  ∫ 4x dx

 

 

      3

2)  ∫ (x²+3x)dx

 

 

     4

3) ∫ (x²-4x+5)dx

Answer 1

Hi Stephanie, it's hard to see whether or not you have definite or indefinite integrals (there are numbers that are floating around the integral signs, but it's hard to tell if they're limits of integration or exponents that belong inside the integral.

 

I'll do my best to answer what I think the questions are... let me know if I mis-interpreted something:

 

(1) [Applying the Power Rule] ∫4x dx = (4x²)/2 + C = 2x² + C, where C is a constant

 

(2) [Applying the Power Rule, term by term] ∫(x² + 3x) dx = x³/3 + + 3x²/2 + C, where C is a constant

 

(3) [Applying the Power Rule, term by term] ∫(x² - 4x + 5) dx = x³/3 - 4x²/2 + 5x + C = x³/3 - 2x² + 5x + C, where C is a constant.

 

Hope this helps!

Let me know if you have any additional questions.

 

Dr. B

mathtutorpros gmail com