Evaluate: a)Π/16b)Π/8c)-Π/2d)Π/4Correct answer is option 'D'. Can you explain this answer?

Question

Evaluate: a)&Pi;/16b)&Pi;/8c)-&Pi;/2d)&Pi;/4Correct answer is option 'D'. Can you explain this answer?

Answer

Answer

Integration of 12-x-x^2 will have maximum value when it's differentiation is zero. differentiation of it is itself 12-x-x^2 . So we can obtain roots of this equation and that will give values of x1 and x2 where integration becomes maximum. roots of x^2-x-12=0 is given by,( -b+or-√b^2-4ac)/2a, which is (-1+√1+48)/2 = 3 and (-1-√1+48)/2 = -4 . So integration from-4 to 3 becomes maximum with -4<3, which='' is='' the='' given='' condition.='' which='' is='' the='' given=''>

Answer

43

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