Question

The area of the region in the first quadrant enclosed by the curves\( y=√x,y=-x+6 \)and the x-axis is 

• A. \(\dfrac{22}{7}\)
• B. \(\dfrac{22}{3}\)
• C. \(12\)
• D. \(24\)
• E. \(8\)

Answer 1

The Correct Option is B

Given that

\(y = √ x,\)    \(y = −x + 6 \)

Then\(\)

\(x = 36 − 12x + x^2\)

\(x^2 − 13x + 36 = 0\)2\(\)

\((x-4)(x-9)=0\)

 \(\therefore x=4 \)and \( x=9\)

represents area of the region in the first quadrant enclosed by the curves y=√x, y = −x+6 and the x-axis

Then, Area\( = ∫_0^6 f(x)dx\)\(\)

\(= ∫_0^6 f(x)dx\)

\(=∫_0^4√xdx+∫_4^6(-x+6)dx\)

\(=[\dfrac{2}{3}x^{\dfrac{3}{2}}]_0^4+[\dfrac{-x^2}{2}+6x]_4^6\)

\(=\dfrac{16}{3} + 18 + 8 − 24 \)

\(= \dfrac{22}{3}\) (_Ans)