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Calculate the area enclosed between the curves y = x 2 and y 2 = x.

Calculate the area enclosed between the curves
y = x2 and y2 = x.

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
7 years ago
Ans:
Hello Student,
Please find answer to your question below

y = x2, y2= x
Intersection of the curves
x4= x
x = 0, 1
Area b/w curves ‘A’
A = \int_{0}^{1}(\sqrt{x}-x^2)dx
A = \int_{0}^{1}\sqrt{x}dx-\int_{0}^{1}x^2dx
A = (\frac{2x^{3/2}}{3})_{0}^{1}-\int_{0}^{1}x^2dx
A = \frac{2}{3}-\int_{0}^{1}x^2dx
A = \frac{2}{3}-(\frac{x^3}{3})_{0}^{1}
A = \frac{2}{3}-\frac{1}{3}
A = \frac{1}{3}

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