Question

# The ratio in which the area bounded by the curve y2=xandx2=y is divided by the line x=12 is

A
421942
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B
32+3942
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C
2131
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D
221331
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Solution

## The correct option is A 4√2−19−4√2Area under a curve f(x) is given by ∫f(x)dx if it is bounded by x=a,x=b lines then area will be ∫baf(x)dxarea bounded by curve y2=x from x=a,x=b is :∫ba√xdxarea bounded by curve y=x2 from x=a,x=b is :∫bax2dxarea bounded by them becomes their difference from the limits given.Here limits will be from x=0,x=12 : ∫120(√x−x2)dx=4√2−124 and x=12,x=1 : ∫112(√x−x2)dx=9−4√224 ratio means just divide them both which gives you;4√2−19−4√2

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