Evaluate the integral. (Use C for the constant of integration.) dx V x2 + 16 Need Help? Read It Watch It Chat About It + -/0.2 points SCalcET7 7.3.013. Evaluate the integral. (Use C for the constant of integration.) V x - 25 dx x3 Need Help? Read It Watch It Chat About It + -/0.2 points SCalcET7 7.3.019. Evaluate the integral. (Remember to use In(| ul) where appropriate. Use C for the constant of 81 + x2 dxThe figure shows a pendulum with length L and the angle 0 from the vertical to the pendulum. It can be shown that 0, as a function of time, satisfies the nonlinear differential equation d'e + 9 sine = 0 dt where g = 9.8 m/s" is the acceleration due to gravity. For small values of 0 we can use the linear approximation sin0 2 0 and then the differential equation becomes linear. Find the equation of motion of a pendulum with length 1 m if @ is initially 0.3 rad and the initial angular velocity is de dt = 2 rad/s . Select the correct answer. O e(t) = 0.3sin ( 9.8 t) + 4 cos (19.8 t) 19.8 O e(t) = 0.3cos (19.8 t) - 19.8 4 sin (19.8 t) O e(t) = 0.3cos (19.8 t) + 2 19.8 sin (19.8 t) O e(t) = 0.3sin ( 9.8 t) + 19.8 cos (19.8 t) O e(t) = 0.3sin (9.8 t) - cos (19.8 t) 19.8Define: proportional model, chi-square goodness of fit test, degrees of freedom, critical value, poisson distribution v . Describe what you can test with a X goodness of fit test Write a paired null and alternate hypothesis for a X goodness of fit test Describe what the chi-square test statistic measures V Describe how you use degrees of freedom in a chi-square test Differentiate between when it is appropriate to use a chi-square distribution, a binomial distribution, or a poisson distribution in a chi-square test v . Identify the assumptions of a chi-square test v Using excel be able to: . Calculate expected frequencies for a chi-square test under a null hypothesis using a proportional model and a poisson distribution Calculate a chi-square test statistic Determine a P-value from a chi-square test statistic