Question

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

Answer 1

 

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

Comments

Sir but answer is 7/6 because below x-axis  area is also valid