Solved: Present Value The board of directors of a corporation is calculating the price

In Exercises 1 8, use the basic integration rules to find or evaluate the integral. 32
2x2x 3 dx

In Exercises 1 8, use the basic integration rules to find or evaluate the integral. 32
2x2x 3 dx

In Exercises 1 8, use the basic integration rules to find or evaluate the integral.

In Exercises 1 8, use the basic integration rules to find or evaluate the integral. 32
2x2x 3 dx

In Exercises 1 8, use the basic integration rules to find or evaluate the integral.

In Exercises 1 8, use the basic integration rules to find or evaluate the integral. 32
2x2x 3 dx

In Exercises 1 8, use the basic integration rules to find or evaluate the integral.

In Exercises 1 8, use the basic integration rules to find or evaluate the integral.

In Exercises 916, use integration by parts to find the integral.e dx 2x sin 3x dx

In Exercises 916, use integration by parts to find the integral.x2 1ex
e dx 2x

In Exercises 916, use integration by parts to find the integral.

In Exercises 916, use integration by parts to find the integral.

In Exercises 916, use integration by parts to find the integral.x 2 1 dx 2 sin 2x dx

In Exercises 916, use integration by parts to find the integral.

In Exercises 916, use integration by parts to find the integral.

In Exercises 916, use integration by parts to find the integral.

In Exercises 1722, find the trigonometric integral cos dx 3x 1 dx

In Exercises 1722, find the trigonometric integral sin2 x 2
cos dx

In Exercises 1722, find the trigonometric integral sec  d 4 x 2 dx

In Exercises 1722, find the trigonometric integral

In Exercises 1722, find the trigonometric integral

In Exercises 1722, find the trigonometric integralcos 2sin  cos 2
d 1

In Exercises 23 and 24, find the area of the region.

In Exercises 23 and 24, find the area of the region.

In Exercises 2530, use trigonometric substitution to find or evaluate the integral.
dx, 12 x24 x2 dx

In Exercises 2530, use trigonometric substitution to find or evaluate the integral.3 x2 9 x
dx,

In Exercises 2530, use trigonometric substitution to find or evaluate the integral.x3 4 x2 dx

In Exercises 2530, use trigonometric substitution to find or evaluate the integral.9 4x2
dx x

In Exercises 2530, use trigonometric substitution to find or evaluate the integral.0 2 4 x2 dx

In Exercises 2530, use trigonometric substitution to find or evaluate the integral.
2 0 sin  1 2 cos2 
d 0

In Exercises 31 and 32, find the integral using each method.

In Exercises 31 and 32, find the integral using each method.

In Exercises 3338, use partial fractions to find the integral.
dx x 28 x2 x 6 dx dv

In Exercises 3338, use partial fractions to find the integral.

In Exercises 3338, use partial fractions to find the integral.

In Exercises 3338, use partial fractions to find the integral.
4x 2 3x 12
dx x2

In Exercises 3338, use partial fractions to find the integral.x2 2x 15 dx

In Exercises 3338, use partial fractions to find the integral.sec2  tan tan  1
d x2

In Exercises 3946, use integration tables to find or evaluate the integral.
dx x 2 3x2 dx
s

In Exercises 3946, use integration tables to find or evaluate the integral.

In Exercises 3946, use integration tables to find or evaluate the integral.

In Exercises 3946, use integration tables to find or evaluate the integral.

In Exercises 3946, use integration tables to find or evaluate the integral.2 4x 8 dx

In Exercises 3946, use integration tables to find or evaluate the integral.3 2x9x2 1 dx,

In Exercises 3946, use integration tables to find or evaluate the integral.

In Exercises 3946, use integration tables to find or evaluate the integral.
1 1 tan x dx

Verify the reduction formula
ln xn dx
xln xn n
ln xn1 dx.
1 1

Verify the reduction formula
tann x dx
1 n 1 tann1 x
tann2 x dx.

In Exercises 4956, find the integral using any method.In Exercises 4956, find the integral using any method.

In Exercises 4956, find the integral using any method.

In Exercises 4956, find the integral using any method.

In Exercises 4956, find the integral using any method.1 x dx x

In Exercises 4956, find the integral using any method.1 cos x dx d

In Exercises 4956, find the integral using any method.

In Exercises 4956, find the integral using any method.

In Exercises 4956, find the integral using any method.

In Exercises 5760, solve the differential equation using any methoddx
9 x2 9

In Exercises 5760, solve the differential equation using any methody dx
4 x2

In Exercises 5760, solve the differential equation using any method

In Exercises 5760, solve the differential equation using any method
1 cos  2

In Exercises 6166, evaluate the definite integral using any method. Use a graphing utility to verify your result.
dx 5 2 xx2 432 dx y

In Exercises 6166, evaluate the definite integral using any method. Use a graphing utility to verify your result.1 0 x x 2x 4
dx 5 2

In Exercises 6166, evaluate the definite integral using any method. Use a graphing utility to verify your result.

In Exercises 6166, evaluate the definite integral using any method. Use a graphing utility to verify your result.

In Exercises 6166, evaluate the definite integral using any method. Use a graphing utility to verify your result.x sin x dx

In Exercises 6166, evaluate the definite integral using any method. Use a graphing utility to verify your result.3 0 x 1 x
dx 

In Exercises 67 and 68, find the area of the region.

In Exercises 67 and 68, find the area of the region.

Centroid In Exercises 69 and 70, find the centroid of the region bounded by the graphs of the equations.y
1 x y
0 2

Centroid In Exercises 69 and 70, find the centroid of the region bounded by the graphs of the equations.x 1 2
4 2 y 2
1, y
x 42 y x 1 2
4 2 y 2

Arc Length In Exercises 71 and 72, approximate to two decimal places the arc length of the curve over the given interval.

Arc Length In Exercises 71 and 72, approximate to two decimal places the arc length of the curve over the given interval.

In Exercises 7380, use LHpitals Rule to evaluate the limit.im x1 ln x2 x 1 y

In Exercises 7380, use LHpitals Rule to evaluate the limit.

In Exercises 7380, use LHpitals Rule to evaluate the limit.

In Exercises 7380, use LHpitals Rule to evaluate the limit.lim x xex2

In Exercises 7380, use LHpitals Rule to evaluate the limit.

In Exercises 7380, use LHpitals Rule to evaluate the limit.

In Exercises 7380, use LHpitals Rule to evaluate the limit.lim  n 10001 0.09 n  n l

In Exercises 7380, use LHpitals Rule to evaluate the limit.im x1  2 ln x 2 x 1 lim

In Exercises 8186, determine whether the improper integral diverges or converges. Evaluate the integral if it converges.
dx 16 0 1  4 x dx

In Exercises 8186, determine whether the improper integral diverges or converges. Evaluate the integral if it converges.
1 0 6 x 1
dx

In Exercises 8186, determine whether the improper integral diverges or converges. Evaluate the integral if it converges.x2 ln x dx

In Exercises 8186, determine whether the improper integral diverges or converges. Evaluate the integral if it converges. 0 e1x x2
dx

In Exercises 8186, determine whether the improper integral diverges or converges. Evaluate the integral if it converges. 1 ln x x2

In Exercises 8186, determine whether the improper integral diverges or converges. Evaluate the integral if it converges. 1 1  4 x
dx

Present Value The board of directors of a corporation is calculating the price to pay for a business that is forecast to yield a continuous flow of profit of $500,000 per year. If money will earn a nominal rate of 5% per year compounded continuously, what is the present value of the business (a) for 20 years? (b) forever (in perpetuity)? (Note: The present value for years is  t0 0 500,000e0.05t t dt.

Volume Find the volume of the solid generated by revolving the region bounded by the graphs of and about the axis.

Probability The average lengths (from beak to tail) of different species of warblers in the eastern United States are approximately normally distributed with a mean of 12.9 centimeters and a standard deviation of 0.95 centimeter (see figure). The probability that a randomly selected warbler has a length between and centimeters is Use a graphing utility to approximate the probability that a randomly selected warbler has a length of (a) 13 centimeters or greater and (b) 15 centimeters or greater. (Source: Petersons Field Guide: Eastern Birds)