Question

The area is included between y² = 4x & ²=4y​

Answer 1

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What is the area enclosed between the curves y^2=4x and x^2 = 4y?

First, where do the curves intersect?

(14x2)2=4x

116x4–4x=0

(x)(116x3–4)=0

x=0;116x3=4

x=0;x3=64

(0,0);(4,4)

These are the two points of intersection. To find the area between the two curves,

∫402x12−14x2dx

43x32−112x3|40

43432−4312

323−163=163

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