Area between lines 2

Calculus Level 2

What is the area bound by the lines y = ( 2 x − 1 ) ( x + 1 ) y=(2x-1)(x+1) , y = − x y=-x , y = − 1 y=-1 , x = 1 2 x=\dfrac 12 and x = 2 x=2 ?


The answer is 7.

Charley Shi by Charley Shi , 19, New Zealand

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1 solution

Poca Poca
Jul 4, 2018

The area below the x x -axis is the area is just 1 + 1 4 + 1 8 = 1.375 1+\frac{1}{4}+\frac{1}{8}=1.375 and the area above it is ∫ 0.5 2 ( 2 x 2 + x − 1 ) d x \int_{0.5}^2{(2x^2+x-1)}dx =5.625. Hence, the total a is 1.375 + 5.625 = 7 1.375+5.625=\boxed{7} .

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