Integrals · Question 11

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The integral 01 -1 (1+x+x2 )dx is equal to :

Answer

(4) 2 -12- 12 e ( 54 )- 2

For x 0: -1 (1+x+x2 )= -1 11+x(x+1)= -1 (x+1)-x1+x(x+1)

= -1(x+1)- -1x

I= 01 -1(x+1) dx- 01 -1x dx= 12 -1u du- 01 -1x dx

By parts: -1u du=u -1u- 12 e (1+u2 )

12 -1u du=2 -12- 12 e5- 4+ 12 e2

01 -1x dx= 4- 12 e2

I=2 -12- 12 e5+ e2- 2

=2 -12- 12 e ( 54 )- 2 ( e2= 12 e4)

Answer: (4)

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