IIT JEE , AIEEE Forum - Mathematics , Integral Calculus

capricornabhi

Dear Sir/madam,

Please help me in the following question:

What value of A & B maximizes and minimizes the value of

_{[ a]}

^{[b ]} (X⁴-2X ²)dx.

Thanx

Abhi

rishikesh_anshu

Simply plot the graph x^4 intersect 2x^2 at 0 and +root 2 and -root 2
so the area bouded by the curve will be max when either a=root2
and b is inf or b=-inf and a is -root 2

for algebric soln differentiat

_{[ a]}

^{[b ]} (X⁴-2X ²)dx. with respect to a and b separatly and apply maxima minima separetly to get appropriate value of a,b separately

iitkgp_bipin

When you will draw the curves x⁴ and 2x² they intersect at (0,0) ; (

2,

2) ; (-

2,

2)

In the 1st quadrant there are two areas one of which is from x = 0 to x =

2 and is bounded and one is unbounded from x =

2 to

Similarly in the 2nd quadrant there are two areas one of which is from =0 to x= -

2 and is bounded and one is unbounded from x = -

2 to -

.

Accordingly set your values of a and b for minimum and maximum.

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