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mathematics
calculus with applications

Questions and Answers of Calculus With Applications

In Exercises 15 through 20, approximate the given integral and estimate the error |En| using(a) The trapezoidal rule(b) Simpson’s rule with the specified number of subintervals. So dx; n = 4
In Exercises 1 through 26, use integration by parts to find the given integral. re² f x ln √x dx
In Exercises 1 through 26, use integration by parts to find the given integral. 10 -2x x(e + ex) dx
In Exercises 1 through 30, either evaluate the given improper integral or show that it diverges. +∞o In x 1² dx
In Exercises 11 through 18, either find a number k such that the given function is a probability density function or explain why no such number exists. f(x) [k(x + 2)-¹ for -1 ≤ x ≤
In Exercises 1 through 30, either evaluate the given improper integral or show that it diverges. +∞0 So 10 -x dx xe¹-
In Exercises 1 through 26, use integration by parts to find the given integral. In x X dx
In Exercises 11 through 18, either find a number k such that the given function is a probability density function or explain why no such number exists. f(x) = xe 0 -kx for x ≥ 0 otherwise
In Exercises 1 through 30, either evaluate the given improper integral or show that it diverges. хр ху- 2xe JO ∞0+.
In Exercises 17 through 20, solve the given initial value problem using either integration by parts or a formula from Table 6.1. Note that Exercises 19 and 20 involve separable differential
In Exercises 21 through 26, determine how many subintervals are required to guarantee accuracy to within 0.00005 in the approximation of the given integral by (a) The trapezoidal rule (b)
In Exercises 17 through 20, solve the given initial value problem using either integration by parts or a formula from Table 6.1. Note that Exercises 19 and 20 involve separable differential
In Exercises 1 through 30, either evaluate the given improper integral or show that it diverges. +00 J2 1 xVln x =dx
In Exercises 19 through 26, f(x) is a probability density function for a particular random variable X. Use integration to find the indicated probabilities.a. P(0 ≤ X ≤ 4)b. P(2 ≤ X ≤ 3)c. P(X
In Exercises 21 through 34, either evaluate the given improper integral or show that it diverges. 10 +00 (1 + 2x)-3/2 dx
In Exercises 1 through 26, use integration by parts to find the given integral. re/ J1/2 t ln 2t dt
In Exercises 21 through 34, either evaluate the given improper integral or show that it diverges. +00 1 1 + 2x dx
In Exercises 15 through 20, approximate the given integral and estimate the error |En| using(a) The trapezoidal rule(b) Simpson’s rule with the specified number of subintervals. 0.6 en e dx; n = 6
In Exercises 1 through 30, either evaluate the given improper integral or show that it diverges. 1 +00 In x X - dx
In Exercises 11 through 16, use the integral table (Table 6.1) to find the given integral. 4 dx x(9 + 5x)
In Exercises 1 through 30, either evaluate the given improper integral or show that it diverges. +00 -Vx e Vx dx
In Exercises 15 through 20, approximate the given integral and estimate the error |En| using(a) The trapezoidal rule (b) Simpson’s rule with the specified number of subintervals. dx; n = 4
In Exercises 11 through 16, use the integral table (Table 6.1) to find the given integral. SAV dx xV4 - x²
In Exercises 11 through 16, use the integral table (Table 6.1) to find the given integral. [ (In 2x)³ dx
In Exercises 15 through 20, approximate the given integral and estimate the error |En| using(a) The trapezoidal rule(b) Simpson’s rule with the specified number of subintervals. S₁ √x dx; n = 10
In Exercises 15 through 20, approximate the given integral and estimate the error |En| using(a) The trapezoidal rule(b) Simpson’s rule with the specified number of subintervals. S²³² x²³ dx; n
In Exercises 1 through 26, use integration by parts to find the given integral. 1 e2x е dx
In Exercises 1 through 26, use integration by parts to find the given integral. Livets dx + 5
In Exercises 1 through 26, use integration by parts to find the given integral. X V 4x + 1 dx
In Exercises 1 through 30, either evaluate the given improper integral or show that it diverges. 0 +00 xe -x dx
In Exercises 1 through 14, approximate the given integral using (a) The trapezoidal rule (b) Simpson’s rule with the specified number of subintervals. - dx; n = 4 X
In Exercises 11 through 18, either find a number k such that the given function is a probability density function or explain why no such number exists. f(x) = [x²³+kx for 0≤x≤2 0 otherwise
In Exercises 11 through 18, either find a number k such that the given function is a probability density function or explain why no such number exists. f(x) = x - kx² for 0 ≤ x ≤ 1 otherwise
In Exercises 11 through 18, either find a number k such that the given function is a probability density function or explain why no such number exists. f(x) = [kx(3x) for 0≤x≤ 3 0 otherwise
In Exercises 11 through 16, use the integral table (Table 6.1) to find the given integral. w²e-w/3 dw
In Exercises 1 through 14, approximate the given integral using (a) The trapezoidal rule (b) Simpson’s rule with the specified number of subintervals. L'e-ve -√x Vx е dx; n = 8
In Exercises 1 through 26, use integration by parts to find the given integral. X √√₂² V2x + 1 dx
In Exercises 1 through 26, use integration by parts to find the given integral. X √x + 2 dx
In Exercises 11 through 18, either find a number k such that the given function is a probability density function or explain why no such number exists. f(x) = [(kx - 1)(x-2) for 0≤x≤
In Exercises 1 through 30, either evaluate the given improper integral or show that it diverges. +∞o -2 xe dx
In Exercises 1 through 30, either evaluate the given improper integral or show that it diverges. •+00 +∞ 2 X Vx² + 2 dx
In Exercises 11 through 16, use the integral table (Table 6.1) to find the given integral. 2 dt 91 9t² + 16
In Exercises 1 through 26, use integration by parts to find the given integral. Ja- x)et dx
In Exercises 1 through 14, approximate the given integral using (a) The trapezoidal rule (b) Simpson’s rule with the specified number of subintervals. S dx V1 + x³ ; n = 6
Use the trapezoidal rule with n = 8 to estimate the value of the integralThen use Table 6.1 to compute the exact value of the integral and compare with your approximation. +√/25 - x² √3 x dx
In Exercises 11 through 18, either find a number k such that the given function is a probability density function or explain why no such number exists. f(x) 4+ 3kx for 0≤x≤ 2 otherwise
In Exercises 11 through 16, use the integral table (Table 6.1) to find the given integral. 5 dx 8 - 21²
In Exercises 1 through 14, approximate the given integral using (a) The trapezoidal rule (b) Simpson’s rule with the specified number of subintervals. √₁ + x² dx; n = 4 1
In Exercises 1 through 14, approximate the given integral using (a) The trapezoidal rule (b) Simpson’s rule with the specified number of subintervals. In x ₁x + 2 dx; n = 4
In Exercises 1 through 26, use integration by parts to find the given integral. fax + (x + 1)(x + 2)6 dx
In Exercises 1 through 30, either evaluate the given improper integral or show that it diverges. +∞o 1² - dx 3 x + 2
In Exercises 11 through 18, either find a number k such that the given function is a probability density function or explain why no such number exists. f(x) = - 3x for 0≤x≤ 1 otherwise
In Exercises 1 through 14, approximate the given integral using (a) The trapezoidal rule (b) Simpson’s rule with the specified number of subintervals. Si dx In x' ;n=6
In Exercises 1 through 26, use integration by parts to find the given integral. 1- x dx
In Exercises 1 through 26, use integration by parts to find the given integral. x(x + 1) dx
In Exercises 1 through 10, use integration by parts to find the given integral. x + 2 e³x dx
In Exercises 1 through 30, either evaluate the given improper integral or show that it diverges. +∞o x² (x³ + 2)² dx
Use the integral table (Table 6.1) to find these integrals. •[ a. C. (In √3x)² dx dx 2√2-9 S b. d. SA dx xV4 + x dx 3x² - 4x
In Exercises 1 through 10, determine whether the given function is a probability density function. f(x) = 0 + 5 for 0≤x≤ 1 otherwise
In Exercises 1 through 26, use integration by parts to find the given integral. fxVx - 6 dx
In Exercises 1 through 14, approximate the given integral using (a) The trapezoidal rule (b) Simpson’s rule with the specified number of subintervals. 2 fee Ma dx; n = 10
In Exercises 1 through 30, either evaluate the given improper integral or show that it diverges. +∞o e¹-x dx ₂1-x
In Exercises 1 through 10, use integration by parts to find the given integral. fav ³√√3x² + 2 dx
In Exercises 1 through 14, approximate the given integral using (a) The trapezoidal rule (b) Simpson’s rule with the specified number of subintervals. Se e dx; n = 4
In Exercises 1 through 10, use integration by parts to find the given integral. W3 1+w² M : dw
In Exercises 1 through 10, determine whether the given function is a probability density function. f(x) = 2 + 2x for 1≤x≤1 otherwise
The useful life of a brand of microwave oven is measured by a random variable X with probability density functionwhere x denotes the time (in months) that a randomly selected oven has been in use.a.
In Exercises 1 through 30, either evaluate the given improper integral or show that it diverges. 10 +00 5e-2x dx
In Exercises 1 through 26, use integration by parts to find the given integral. we0.1w dw ve
In Exercises 1 through 14, approximate the given integral using (a) The trapezoidal rule (b) Simpson’s rule with the specified number of subintervals. S V9x² dx; n = 6
In Exercises 1 through 10, determine whether the given function is a probability density function. f(x) = 0 Vx for 0≤x≤9 otherwise
In Exercises 1 through 10, use integration by parts to find the given integral. 1₂ (2x + 1)(x + 3)3/2 dx -2
Suppose that the monorail from Newark Liberty Airport to New York City leaves every hour. Let X be the random variable that represents the time in minutes a person arriving at the monorail terminal
In Exercises 1 through 10, use integration by parts to find the given integral. (In x)² dx
In Exercises 1 through 30, either evaluate the given improper integral or show that it diverges. +00 ex dx
In Exercises 1 through 26, use integration by parts to find the given integral. Sve ve -v/5 dv
In Exercises 1 through 10, determine whether the given function is a probability density function. f(x) xe lo -X for x ≥ 0 for x < 0
Zain, a patient in a hospital, receives 0.7 mg of a certain drug intravenously every hour. The drug is eliminated exponentially in such a way that the fraction of drug that remains in Zain’s body
In Exercises 1 through 30, either evaluate the given improper integral or show that it diverges. √3 +00 1 (2x - 1)² dx
In Exercises 1 through 10, determine whether the given function is a probability density function. f(x): 2 -2x for x ≥ 0 for x < 0
In Exercises 1 through 14, approximate the given integral using (a) The trapezoidal rule (b) Simpson’s rule with the specified number of subintervals. -1 V1 + x² dx; n = 4
In Exercises 1 through 14, approximate the given integral using (a) The trapezoidal rule (b) Simpson’s rule with the specified number of subintervals. 1 2 x – 1 dx; n = 4 -
In Exercises 1 through 26, use integration by parts to find the given integral. t In t² dt
In Exercises 1 through 30, either evaluate the given improper integral or show that it diverges. +∞o J3 1 √/2x-1 dx
In Exercises 1 through 26, use integration by parts to find the given integral. St t In 2t dt
It is estimated that t years from now an office building will be generating profit for its owner at the rate of R(t) = 50 + 3t thousand dollars per year. If the profit is generated in perpetuity and
In Exercises 1 through 10, use integration by parts to find the given integral. In Vs Vs ds
In Exercises 1 through 30, either evaluate the given improper integral or show that it diverges. •+∞o 1 2x 3 1 -dx
In Exercises 1 through 10, determine whether the given function is a probability density function. 10 f(x)= (x + 10)² 0 for x ≥ 0 for x < 0
In Exercises 1 through 14, approximate the given integral using (a) The trapezoidal rule (b) Simpson’s rule with the specified number of subintervals. 1 SO₁+R² Jo 1 + x² dx; n = 4
In Exercises 1 through 10, determine whether the given function is a probability density function. f(x): X 2 for 1 ≤ x ≤ 2 otherwise
In Exercises 1 through 10, use integration by parts to find the given integral. -9 y dy V4 - 5y
An investment of $10,000 is projected to grow at an annual rate equal to 5% of its size at any time t. What will the investment be worth in 10 years?
In Exercises 1 through 30, either evaluate the given improper integral or show that it diverges. 1 -00 -2/3 X dx
In Exercises 1 through 10, use integration by parts to find the given integral. fxv2x xV2x + 3 dx + 3 dx
In Exercises 1 through 26, use integration by parts to find the given integral. -X (3-2x)e dx
After t hours on the job, a factory worker can produce 100te−0.5t units per hour. How many units does a worker who arrives on the job at 8:00 A.M. produce between 10:00 A.M. and noon?
In Exercises 1 through 10, determine whether the given function is a probability density function. f(x) = (7 4 2x) for 1 ≤x≤5 otherwise
In Exercises 17 through 20, solve the given initial value problem using either integration by parts or a formula from Table 6.1. Note that Exercises 19 and 20 involve separable differential
In each case, either evaluate the given improper integral or show that it diverges. a. C. +∞o 1 Si +00 36 1 dx X (x + 1)² dx b. d. +00 Si -2x xe dx +00 ľ -1² xe dx

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