Question

Attachement. Please help. I keep getting 8/3, but the correct answer is 9/2.

Answer 1

where did i go wrong?

Answer 2

(-1)^3 is -1 and when you subtract the -1/3 it becomes a +1/3 that is added.

Answer 3

if I fixed that, would it give me 9/2? or did I do something else wrong also?

Answer 4

Find the definate integral for x^2+1 from -1 to 2. Then Subtract (2) for the region of y=x [0,2] and add 1/2 for y=x [-1,0]. I get the following: \[\int\limits_{-1}^{2}(x ^{2}+1)dx=\frac{ 2 ^{3} }{3 }+2-\left( \frac{ (-1) ^{3} }{ 3 }+(-1) \right)\]
\[=\frac{ 8 }{3 }+2-(\frac{ -1 }{ 3 }-1)=\frac{ 9 }{ 3 }+3=6\]
\[6-2+\frac{ 1 }{ 2 }=4\frac{ 1 }{ 2 }=\frac{ 9 }{ 2 }\]

Answer 5

alright, thank you so much. I understand now :D