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Question

Let 'a' be a positive constant number. Consider two curves C1:y=ex,C2:y=eax. Let S be the area of the part surrounded by C1,C2 and the y-axis, then

A
limaS=1
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B
lima0Sa2=14
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C
Range of S is (0,)
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D
S(a) is neither odd nor even
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Solution

The correct option is B lima0Sa2=14
C1:y=ex,C2:y=eax
Point of intersection
ex=e(ax)
x=a2,y=ea2
S=a20C2dxa20C1dx
S=a20eaxdxa20exdx=[eax]a20[ex]a20
S=(ea2ea)(ea21)=(ea2ea2+1)=(ea21)2
lima0sa2=⎢ ⎢ ⎢ ⎢(ea21)2a2⎥ ⎥ ⎥ ⎥a24a2=14


861952_260794_ans_e3228a996b894bbb88da0ac636fdd98e.png

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