Consider the region R = { ( x , y ) : x ≤ y ≤ 9 − 3 11 x 2 , x ≥ 0 } . The area, of the largest rectangle of sides parallel to the coordinate axes and inscribed in R , is:

Question

Consider the region R = { ( x , y ) : x ≤ y ≤ 9 − 3 11 ​ x 2 , x ≥ 0 } . The area, of the largest rectangle of sides parallel to the coordinate axes and inscribed in R , is:

TestHub · Accepted Answer

t . ( 9 − 3 11 t 2 ​ − t ) ​ A = 9 t − t 2 − 3 11 ​ t 3 dt dA ​ = 9 − 2 t − 11 t 2 ⇒ 11 t 2 + 2 t − 9 = 0 11 t 2 + 11 t − 9 t − 9 = 0 t = − 1& t = 11 9 ​ ​ ​ ∴ largest area = 11 9 ​ ( 9 − 3 11 ​ , 121 81 ​ − 11 9 ​ ) = 11 9 ​ ⋅ 11 63 ​ = 121 567 ​ ​

Mathematics - Area under the curve Question with Solution | TestHub

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