### Home > APCALC > Chapter 10 > Lesson 10.2.1 > Problem10-112

10-112.

Calculate the area bounded by the curve $y =\sqrt { x }$, the line tangent to the curve at $x = 9$, and the $y$-axis.

$y^\prime=\frac{1}{2\sqrt{x}}\text{, so }y^\prime(9)=\frac{1}{6}$

The line passes through the point $(9, 3)$ and has a slope of $1/6$.

Graph the functions or use algebra to determine the bounds of integration/points of intersection.

$A=\int_0^9 \Big(\frac{1}{6}(x-9)+3-\sqrt{x}\Big)dx$