Find the area of the region enclosed by the curves y²=x, x=1/4, y=0 and x=1, using integration.

Bounded area = ∫limits_(1/4)¹ y dx = ∫limits_(1/4)¹sqrt x dx = 2/3[x^(3/2)]_(1/4)¹ = 2/3(1-1/8) = 7/3×7/8 = 7/12 square units

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Chapter: 2022· JEE

Find the area of the region enclosed by the curves \( y^{2}=x, x=\frac{1}{4}, y=0 \) and \( x=1 \), using integration.

Doubtly Asked 25 Jun 2022 Student doubt Save WhatsApp Report

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Best answer

Bounded area

= \(\int\limits_{1/4}^1\)y dx

= \(\int\limits_{1/4}^1\sqrt x\)dx

= \(\frac23[x^{3/2}]_{1/4}^1\)

= \(\frac23(1-\frac18)\) = \(\frac73\times\frac78\) = 7/12 square units

Doubtly · 25 Jun 2022 Report

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