1. ## Two quick Questions...

1.

The base of a certain solid is the area bounded above by the graph of y =f(x) =25 and below by the graph of y= g(x)= 16x^2. Cross-sections perpendicular to the x axis are squares.

Use the formula $
V = \int_a^b A(x)dx
$

Thus the volume of the solid is V= ?

2.

To find the length of the curve defined by

y = 2x^2 +3x

from the point (0,0) to the point (1,5), you'd have to compute

$\int_a^b f(x)dx
$

where a = ?
where b = ?

and f(x)= ?

Thanks As always

qbkr21

2. Hello, qbkr21!

Here's help with #2 . . .

2) To find the length of the curve defined by: . $y \:= \:2x^2 +3x$ .from (0,0) to (1,5)

you'd have to compute: . $\int_a^b f(x)\ dx$ . . . where $a = ?$ . where $b = ?$ . and $f(x)= ?$
You're expected to know the Arc Length formula: . $L \;=\;\int^b_a\sqrt{1 + \left(\frac{dy}{dx}\right)^2}\,dx$

Since $\frac{dy}{dx} \:=\:4x + 3$, then: . $1 + \left(\frac{dy}{dx}\right)^2\:=\:1 + (4x + 3)^2 \;=\;16x^2 + 24x + 10$

. . Therefore: . $L \;=\;\int^5_1\sqrt{16x^2 + 24x + 10}\,dx$

Can you answer the questions now?