5.5 Homework - Substitution Rule (Homework)

6. [-/1 Points] DETAILS SCALCET9 5.5.065. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Evaluate the definite integral. 1 dx Need Help? Read It 7. [-/1 Points] DETAILS SCALCET9 5.5.066. MY NOTES ASK YOUR TEACHER Evaluate the definite integral. ex 1 + 2x x Need Help? Read It 8. [-/1 Points] DETAILS SCALCET9 5.5.077. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Evaluate the definite integral. - dz ez + 9z Need Help? Read It Watch It9. [-/1 Points] DETAILS SCALCET9 5.5.090.EP. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER The rate of growth of a fish population was modeled by the equation 90,000e -0.6t G(t) = (1 + 5e-0.6t )2 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. 90,000e -0.6t 1 + 5e-0.6t 2 dt Find a substitution and apply it to rewrite the integrand in the form - 12 du. 1 + 5e -12 If the biomass was 10,000 kg in the year 2000, what is the predicted biomass (in kg) for the year 2020? (Round your answer to the nearest whole number.) J kg Need Help? Read It10. [-/1 Points] DETAILS SCALCET9 5.5.097. MY NOTES ASK YOUR TEACHER If a and b are positive numbers, show that Let u = 1 - x. Then, x = and du = ? v . Use this substitution to rewrite the integral in terms of u. 10 x8 ( 1 - x )6 ax = [ ub ( - du ) = (1 - u)=du Then, replacing u with x results in the integral, ( 1 - x ) 'dx . Need Help? Read It Watch It