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Use limits of definite integrals to calculate each of the improper integrals in Exercises.

042x-4x2-4x+3dx

Short Answer

Expert verified

The improper integral on [0,4]diverges.

042x-4x2-4x+3dx=

Step by step solution

01

Step 1. Given information. 

The given integral is the following.

042x-4x2-4x+3dx

02

Step 2. Value of integral. 

The function f(x)=2x-4x2-4x+3has a vertical asymptote at x=1,3

solve this improper integral by splitting at x=1,3.

localid="1648884400399" 042x-4x2-4x+3dx=012x-4x2-4x+3dx+132x-4x2-4x+3dx+342x-4x2-4x+3dx

As we know thatlocalid="1648884235145" 011x2dxis diverse and integral of functions less than 1x2will be diverse.

and 2x-4x2-4x+3>1x2so localid="1648891997358" 012x-4x2-4x+3dxis diverse.

So042x-4x2-4x+3dxis also diverse.

042x-4x2-4x+3dx=

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