5.5 Homework - Substitution Rule (Homework)

1. [0.66/1 Points] DETAILS PREVIOUS ANSWERS SCALCET9 5.5.005.EP. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Consider the following integral. 178 - 6 dx Given the substitution u = x - 6, find du. du = 6.x5 ox Rewrite the given integral in terms of u. 1 du Evaluate the integral by making the given substitution. (Remember to use absolute values where appropriate. Use C for the constant of integration.) - log (x 6 - 6) +c X Need Help? Read It4. [0/1 Points] DETAILS PREVIOUS ANSWERS SCALCET9 5.5.015.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Evaluate the indefinite integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) dx 4x + 5 log (4x + 5 ) + C X Need Help? Read It Watch It Master It6. [0/1 Points] DETAILS PREVIOUS ANSWERS SCALCET9 5.5.065. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Evaluate the definite integral. 1/x - dx 1.6 + u X Enhanced Feedback Please try again. Recall the substitution rule for definite integrals: If g' is continuous on [a, b] and fis continuous on the range of u = g(x), then / Ag(x))g'(x)dx = / Rujdu. Try letting u be the expression within the exponent of e. Need Help? Read It 7. [0/1 Points] DETAILS PREVIOUS ANSWERS SCALCET9 5.5.066. MY NOTES ASK YOUR TEACHER Evaluate the definite integral. 1 + @ 2x 0.4328 X Need Help? Read It8. [0/1 Points] DETAILS PREVIOUS ANSWERS SCALCET9 5.5.077. Evaluate the definite integral. e- + 9 dz ez + 92 2.4611 X9. [0.8/1 Points] DETAILS PREVIOUS ANSWERS 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. 20 90,000e -0.6t (1 + 5e-0.6t )2 dt Find a substitution and apply it to rewrite the integrand in the form -2 du. -30000 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.) kg Need Help? Read It