`int_1^2(1 + 2y)^2dy` Evaluate the integral.

Textbook Question

Chapter 5, 5.3 - Problem 33 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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gsarora17 | (Level 2) Associate Educator

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`int_1^2(1+2y)^2dy`

`=int_1^2((1)^2+2*2y*1+(2y)^2)dy`

`=int_1^2(1+4y+4y^2)dy`

`=[y+4y^2/2+4y^3/3]_1^2`

`=[y+2y^2+(4y^3)/3]_1^2`

`=[2+2(2)^2+(4(2^3))/3]-[1+2(1)^2+(4(1)^3)/3]`

`=[2+8+32/3]-[1+2+4/3]`

`=((30+32)/3)-((9+4)/3)`

`=49/3`

 

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