One of the roots of the equation f ( x ) = 0 is an even prime integer where f ( x ) = x 2 − a x + b ('a' is an odd positive integer). Also known that ∑ i = 1 5 f ( i ) = 20 and two curves

Question

One of the roots of the equation f ( x ) = 0 is an even prime integer where f ( x ) = x 2 − a x + b ('a' is an odd positive integer). Also known that ∑ i = 1 5 ​ f ( i ) = 20 and two curves are defined as C 1 ​ : y 2 = f ( x ) and C 2 ​ : y 2 = − f ( x ) . The smaller area bounded by y = f ( x ) and curve C 2 ​ is 6 λ 3 π − λ ​ units then ' λ ' equals.

TestHub · Accepted Answer

f ( x ) = x 2 − 3 x + 2 and C 2 ​ is the circle ( x − 2 3 ​ ) 2 + y 2 = 4 1 ​ , which meets y = f ( x ) at (1,0) and (2, 0). Required Area = (upper semicircle area) − ∫ 1 3/2 ​ ( x 2 − 3 x + 2 ) d x = 8 π ​ − 6 1 ​ = 24 3 π − 4 ​

Mathematics - Application of Derivative Question with Solution | TestHub

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