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)