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Question

Find the area of the region bounded by the parabolas y2=4x and x2=4y.

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Solution

y2=4x x=y24 --- (i)
x2=4y --- (ii)

Substitute (i) in (ii),
(y24)2=4y

y416=4y y3=64 y=4

x=y24=424=4

Thus the parabolas intersect at (4,4) and (0,0)

Area=40ydx=40(yp1yp2)dx=40(4xx24)dx
=40(2xx24)dx

=∣ ∣2x3232x34(3)∣ ∣40

=(43(4)324312)(0)

Area=5.33sq.unit

1182299_1435824_ans_b725f220e94849d094f3aaa3a4fd1e9b.png

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