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Question

Figure shows the curve y=x2.Find the area of the shaded part between x=0 and x=6


A

216 unit2

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B

72 unit2

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C

12 unit2

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D

None of these

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Solution

The correct option is B

72 unit2


The area can be divided into strips by drawing ordinates between x = 0 and x = 6 at a regular interval of dx. Consider the strip between the ordinates at x and x + dx. The height of this strip is y=x2. The area of this strip is dA = y dx = x2dx.

The total area of the shaded part is obtained by summing up these strip-areas with x varying from 0 to 6. Thus

A=60x2 dx

=[x33]60=21603=72


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