Certain indefinite integrals such as |dx cannot be expressed in finite terms using elementary functions. When such an integral is encountered while solving a differential equation, it is often helpful to use definite integration (integrals with variable upper limit) Use separation of variables and definite integration to find an explicit solution to the initial value problems in parts a-c, and use Simpson's rule with n 4 to approximate an answer to part b at x 0.5 to three decimal laces. Click the icon to view an example of this process. a. Soive the initial vlue problem y se, with ylo)-0. Use t as the variable of integration in the explicit solution y(x)=
b. Solve the initial value probemywith y(0)-1. Use t as the variable of integration in the explicit solution. y(x)= dy
c. Sove the initial value problem d "Y sin x 1 + with y(0)" 1 Use t as the variable of integration in the explicit solution.
d. Use Simpson's rule with n 4 to approximate the solution to part b at x 0.5 to three decimal places 2Click the icon to review Simpson's rule.