CPM Homework Help : APCALC Problem 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.

Step 1:

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

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

Step 2:

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

Step 3:

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