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Biocalculus Calculus Probability And Statistics For The Life Sciences 1st Edition James Stewart, Troy Day - Solutions
y1 0y e2y dy Evaluate the integral.
y9 4ln y sy dy Evaluate the integral.
y2 1ln x x2 dx Evaluate the integral.
y1 0sx2 1 1de2x dx Evaluate the integral.
y 0 t sin 3t dt Evaluate the integral.
y e2 cos 2 d Evaluate the integral.
y e2 sin 3 d Evaluate the integral.
y p5 ln p dp Evaluate the integral.
y ln s3 x dx Evaluate the integral.
y x2 cos mx dx Evaluate the integral.
y x2 sin x dx Evaluate the integral.
y t sin 2t dt Evaluate the integral.
y rery2 dr Evaluate the integral.
y xe2x dx Evaluate the integral.
y x cos 5x dx Evaluate the integral.
y cos d ; u − , dv − cos d Evaluate the integral using integration by parts with the indicated choices of u and dv.
y x2 ln x dx; u − ln x, dv − x2 dx Evaluate the integral using integration by parts with the indicated choices of u and dv.
If a and b are positive numbers, show that - xp(x 1)qx f = xp q (x 1),x J
If f is continuous on R, prove thatFor the case where f sxd > 0, draw a diagram to interpret this equation geometrically as an equality of areas. So f(x + c) dx = f(x) dx Jate
If f is continuous and y4 0f sxd dx − 10, find y2 0f s2xd dx.
If f is continuous and y9 0f sxd dx − 4, find y3 0xf sx2 d dx.
Growing degree days The rate of development of many plant species depends on the temperature of the environment in such a way that maturity is reached only after a certain number of “degree-days.” Suppose that temperature T as a function of time t is given bywhere t is measured in days. If
Photosynthesis The rate of primary production refers to the rate of conversion of inorganic carbon to organic carbon via photosynthesis. It is measured as a mass of carbon fixed per unit biomass, per unit time. A common model for this relationship is PsId −aI s1 1 bI 2 where P is the rate of
Gompertz tumor growth In Chapter 7 we will explore a model for tumor growth in which the growth rate is given by tstd − 212e2te2t ln 2 mm3ymonth By how much is the volume of the tumor predicted to increase over the first year?
Dialysis treatment removes urea and other waste products from a patient’s blood by diverting some of the bloodflow externally through a machine called a dialyzer. The rate at which urea is removed from the blood (in mgymin) is often well described by the equation cstd −K Vc0e2KtyV where K is
Breathing is cyclic and a full respiratory cycle from the beginning of inhalation to the end of exhalation takes about 5 s. The maximum rate of air flow into the lungs is about 0.5 Lys. This explains, in part, why the function f std − 12 sins2 ty5d has often been used to model the rate of air
Fish biomass The rate of growth of a fish population was modeled by the equationwhere t is measured in years since 2000 and G in kilograms per year. If the biomass was 25,000 kg in the year 2000, what is the predicted biomass for the year 2020? G(t) 60,000e-0.61 (1 + 5e-0.6)2
An oil storage tank ruptures at time t − 0 and oil leaks from the tank at a rate of rstd − 100e20.01t liters per minute. How much oil leaks out during the first hour?
A bacteria population starts with 400 bacteria and grows at a rate of rstd − s450.268de1.12567t bacteria per hour. How many bacteria will there be after three hours?
Which of the following areas are equal? Why? 0 6 y. y=ex y y=2xe* y= esinx sin 2x 1x 0 1x 0 Plat TT X
Evaluate y1 0 xs1 2 x4 dx by making a substitution and interpreting the resulting integral in terms of an area.
Evaluate y2 22 sx 1 3ds4 2 x2 dx by writing it as a sum of two integrals and interpreting one of those integrals in terms of an area.
Verify that f sxd − sin s3 x is an odd function and use that fact to show that 0sin x dx = 1
y1 0dx s1 1 sx d4 Evaluate the definite integral.
yTy2 0sins2 tyT 2 d dt Evaluate the definite integral.
y1 0ez 1 1 ez 1 z dz Evaluate the definite integral.
ya 0xsa2 2 x2 dx Evaluate the definite integral.
y2 1xsx 2 1 dx Evaluate the definite integral.
y y2 2 y2 x2 sin x 1 1 x6 dx Evaluate the definite integral.
y y4 2 y4 sx3 1 x4 tan xd dx Evaluate the definite integral.
y y2 0cos x sinssin xd dx Evaluate the definite integral.
y4 1esx sx dx Evaluate the definite integral.
y1y2 1y6 csc t cot t dt Evaluate the definite integral.
y1 0x2s1 1 2x3d5 dx Evaluate the definite integral.
ys 0 x cossx2d dx Evaluate the definite integral.
y1 0s3 1 1 7x dx Evaluate the definite integral.
y1 0s3t 2 1d50 dt Evaluate the definite integral.
y1 0coss ty2d dt Evaluate the definite integral.
y x1 1 x4 dx Evaluate the indefinite integral.
y 1 1 x 1 1 x2 dx Evaluate the indefinite integral.
y sin x 1 1 cos2x dx Evaluate the indefinite integral.
y sin 2x 1 1 cos2x dx Evaluate the indefinite integral.
y ex ex 1 1 dx Evaluate the indefinite integral.
y xs2x 1 5d8 dx Evaluate the indefinite integral.
y x2s2 1 x dx Evaluate the indefinite integral.
y sec3x tan x dx Evaluate the indefinite integral.
y dt cos2 ts1 1 tan t Evaluate the indefinite integral.
y e2r sinse2rd dr Evaluate the indefinite integral.
y coss yxd x2 dx Evaluate the indefinite integral.
y scot x csc2x dx Evaluate the indefinite integral.
y sinsln xd xdx Evaluate the indefinite integral.
y sx2 1 1dsx3 1 3xd4 dx Evaluate the indefinite integral.
y cos x sin2x dx 22. y tan21x 1 1 x2 dx Evaluate the indefinite integral.
y sec 2 tan 2 dEvaluate the indefinite integral.
y exs1 1 ex dx Evaluate the indefinite integral.
y z 2 z 3 1 1 dz Evaluate the indefinite integral.
y a 1 bx2 s3ax 1 bx3 dx Evaluate the indefinite integral.
y sin sx sx dx Evaluate the indefinite integral.
y dx 5 2 3x Evaluate the indefinite integral.
y xsx2 1 1d2 dx Evaluate the indefinite integral.
y sln xd2 xdx Evaluate the indefinite integral.
y ex cossexd dx Evaluate the indefinite integral.
y sin t dt Evaluate the indefinite integral.
y s3t 1 2d2.4 dt Evaluate the indefinite integral.
y s3x 2 2d20 dx Evaluate the indefinite integral.
y x2sx3 1 5d9 dx Evaluate the indefinite integral.
y x sins x2d dx Evaluate the indefinite integral.
y sec2s1yxd x2 dx, u − 1yx Evaluate the integral by making the given substitution.
y cos3 sin d, u − cos Evaluate the integral by making the given substitution.
y dt s1 2 6td4 , u − 1 2 6t Evaluate the integral by making the given substitution.
y x2sx3 1 1 dx, u − x3 1 1 Evaluate the integral by making the given substitution.
y x3s2 1 x4d5 dx, u − 2 1 x4 Evaluate the integral by making the given substitution.
y e2x dx, u − 2x Evaluate the integral by making the given substitution.
Find a function f and a number a such that 6+ f(t) fdt=2x J+9 for all x > 0
Evaluate the limit by first recognizing the sum as a Riemann sum for a function defined on f0, 1g. 84. lim ++ +) 3 n + n n
Evaluate the limit by first recognizing the sum as a Riemann sum for a function defined on f0, 1g. 83. lim i= n
The area labeled B is three times the area labeled A. Express b in terms of a. y y= ex YA y=ex 0 A a x B b x
Suppose h is a function such that hs1d − 22, h9s1d − 2, h0s1d − 3, hs2d − 6, h9s2d − 5, h0s2d − 13, and h0 is continuous everywhere. Evaluate y2 1 h0sud du.
The error functionis used in probability, statistics, and engineering.(a) Show that yb a e2t 2 dt − 12 s ferfsbd 2 erfsadg.(b) Show that the function y − ex 2erfsxd satisfies the differential equation y9 − 2xy 1 2ys . erf(x) = 2 Jo -12 dt
If f s1d − 12, f 9 is continuous, and y4 1 f 9sxd dx − 17, what is the value of f s4d?
Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. 78. y = for sin Losint dt
Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. 'tan x 77. y = + t di 1 = Jo dt
Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. 76. h(x)=1+r dr
Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. 75. h(x)= 1/x arctant dt 2
Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. 74. G(x) = cos t dt
Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. 73. F(x)=1+ sec t dt Hint: 1+ sect dt = 1 + sec t dt
tsrd − yr 0sx2 1 4 dx Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.
tsyd − yy 2t 2 sin t dt Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.
tsxd − yx 3et 22t dt Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.
tsxd − yx 11 t 3 1 1 dt Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.
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