Solve this 4 questions (Applied Mathematics)

1. Evaluated the area between the curves over the stated interval Y1= x3-5x+10 and Y2= X'- from x = 0 to x=7. Ranging x from 0 to 3 and 3 to 5. (Plot the graph) 10 2. Use the formula for the general solution to solve the following equation. a. Dyfdt 4y = 16 10 3. Integration by parts 10 marks 4-K; 3* _ (a +3)3 (1:: 4. Find the critical values of the two good produced in the rm given that it minimizes the cost, given the cost function C= x2 +2xz + 42 and the fnm is bound by contract to produce minimum combination subject to constraint x+z = 12. 20 marks