calculate the integral (2x - 4x3) dx

Question

Can you help me calculate the integral ∫²₁ (2x - 4x³⁾ dx ?

And show me the steps to get there? 

Thanks!

Answer 1

The integrand is the sum of two terms, each one of which is a power of x.     

  The anti derivative of  xⁿ  is   xⁿ⁺¹ /(n+1)     So  ∫ x dx =  x²/2  and  ∫ x³ =  x⁴/4.

 

   So with this information the desired definite integral is

 

   2 x² /2  |² ₁   - 4 x⁴ /4 |² ₁     =   (2² - 1²)  -  (2⁴ - 1⁴)  =   3- 15 = -12