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#### paulmdrdo

##### Active member

- May 13, 2013

- 386

1. find the area of the bounded region by the curve y=9-x^2 and the x-axis.

soln.

$\displaystyle 9-x^2=0$ the roots or points of intersection are x=3,-3

calculating

$\displaystyle\int_{-3}^3 (9-x^2)dx$ = $\displaystyle \left[9x-\frac{x^3}{3}\right]_{-3}^3$

my answer is 36 sq. units.

2. find the area bounded by ln(x) and x-axis with x=2 and x=4.

soln.

$\displaystyle \int_{2}^4 ln(x)dx=\left[xlnx-x\right]_{2}^4$

my answer is 2.158 sq. units

3. find the area bounded by sin(x), x-axis, x=(1/3)pi, x=(2/3)pi

$\displaystyle\int_{\frac{1}{3}\pi}^{\frac{2}{3} \pi}\sin(x)dx=[-\cos(x)]_{\frac{1}{3}\pi}^{\frac{2}{3} \pi}$

my answer is 1 sq. units