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Approximate the integral by the trapezoidal rule.
1
0
x3exdx; n = 4
Express your answer to four decimal places.
A money market fund has a continuous flow of money at a rate of 0.09x +700 dollars for 10 years.
Find the present value of this flow if interest is earned at 4% compounded continuously.
Evaluate the integral using integration by parts.
eax a sin bx – b cos bx
a2+b2+ C
Determine the integral by making an appropriate substitution.
Evaluate the integral using integration by parts.
Determine the integral by making an appropriate substitution.
Evaluate the integral using integration by parts.
1
13 e2x(2 sin 3x – 3 cos 3x) + C
1
13 e2x(sin 3x – 3 cos 3x) + C
–e2x(sin 3x – 3 cos 3x) + C
An investment is expected to produce a uniform continuous rate of money flow of $500 per year for
10 years. Find the present value at 6% compounded continuously.
Determine the integral by making an appropriate substitution.
Evaluate the integral using integration by parts.
Evaluate the improper integral whenever it is convergent. If it is divergent, state this.
Divide the interval into n subintervals and list the value of
x and the midpoints x1, … , xn of the subintervals.
x = 0.5; x1= – 7.5, x2= – 7.25, x3= – 6.75, x4= – 6.25, x5= – 5.75, x6= – 5
x = 0.25; x1= – 7.75, x2= – 7.25, x3= – 6.75, x4= – 6.25, x5= – 5.75, x6= – 5.25
x = 0.5; x1= – 7.75, x2= – 7.25, x3= – 6.75, x4= – 6.25, x5= – 5.75, x6= – 5.25
x = 0.5; x1= – 7.5, x2= – 7, x3= – 6.5, x4= – 6, x5= – 5.5, x6= – 5
Determine the integral by making an appropriate substitution.
Approximate the integral by the trapezoidal rule.
The following data give the marginal cost for different levels of production at Zipperty–Doo–Dah
Inc. Here x represents the number of zippers produced and C'(x) is in dollars per zipper.
Approximate the total in going from a production level of 50 zippers to 90 zippers.
x50 60 70 80 90
C'(x) 4.5 5.0 5.3 5.8 6.5
Determine the integral by making an appropriate substitution.
Evaluate the integral using integration by parts.
Determine the integral by making an appropriate substitution.
sin cos2
1 +cos3
The rate of a continuous money flow is 1000e–.4 dollars per year for 10 years. Find the present
value if interest is earned at 3% compounded continuously.
Consider
1/2
0
f(x)dx, where f(x) =e–2x. Find a number A such that f(x) A for all x
satisfying 0 x 1
2. Use this A to obtain a bound on the error of using Simpson’s rule with n =5 to
approximate the definite integral.
Consider
2
0
f(x)dx, where f(x) =1
20 x5+2x2. Find a number A such that f(x) A for all x
satisfying 0 x 2. Use this A to obtain a bound on the error of using the midpoint rule with n =8
to approximate the definite integral.
Determine the integral by making an appropriate substitution.