Consider the following integral. dx Given the substitution u x6-8, find du. du= 1) dx Rewrite...

 

   

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Consider the following integral. dx Given the substitution u x6-8, find du. du= 1) dx Rewrite the given integral in terms of u. ((6-8) + C ) du Evaluate the integral by making the given substitution. (Remember to use absolute values where appropriate. Use C for the constant of integration.) Consider the following integral. eu du (9-e4)2 Find a substitution to rewrite the integrand as x = dx = 1) du dx. Evaluate the given integral. (Use C for the constant of integration.) The rate of growth of a fish population was modeled by the equation G(t)= 30,000e-0.6t + 5e-0.6) 2, (1+5 where t is measured in years since 2000 and G in kilograms per year. Write an integral to find the change in the population predicted between 2000 and 2020. 30,000e-0.6t 1+5e-0.6t dt Find a substitution and apply it to rewrite the integrand in the form du. 1+5e-12 du If the biomass was 30,000 kg in the year 2000, what is the predicted biomass (in kg) for the year 2020? (Round your answer to the nearest whole number.) kg If a and b are positive numbers, show that xb(1-x)dx. and du-dx 0 x Let u=1-x. Then, x = 0 Use this substitution to rewrite the integral in terms of u. x (1-x) xa (1-x)b dx = 19 ub (-du)= ub(1 - u) du Then, replacing u with x results in the integral, (1-x) dx. Consider the following integral. dx Given the substitution u x6-8, find du. du= 1) dx Rewrite the given integral in terms of u. ((6-8) + C ) du Evaluate the integral by making the given substitution. (Remember to use absolute values where appropriate. Use C for the constant of integration.) Consider the following integral. eu du (9-e4)2 Find a substitution to rewrite the integrand as x = dx = 1) du dx. Evaluate the given integral. (Use C for the constant of integration.) The rate of growth of a fish population was modeled by the equation G(t)= 30,000e-0.6t + 5e-0.6) 2, (1+5 where t is measured in years since 2000 and G in kilograms per year. Write an integral to find the change in the population predicted between 2000 and 2020. 30,000e-0.6t 1+5e-0.6t dt Find a substitution and apply it to rewrite the integrand in the form du. 1+5e-12 du If the biomass was 30,000 kg in the year 2000, what is the predicted biomass (in kg) for the year 2020? (Round your answer to the nearest whole number.) kg If a and b are positive numbers, show that xb(1-x)dx. and du-dx 0 x Let u=1-x. Then, x = 0 Use this substitution to rewrite the integral in terms of u. x (1-x) xa (1-x)b dx = 19 ub (-du)= ub(1 - u) du Then, replacing u with x results in the integral, (1-x) dx.