PrOblem #1: The curve y = wig -x2= 2 E x 5 2, is rotated about the x-axjs. Find the area of the resulting surface. Problem #2: The below curve is rotated about the y-axis. Find the area of the resulting surface. = 16 2, 15x52 2 (A) 1 2x2 )dx (B) | 2x (x 4x2 [) dx (C) 2n + )dx 1 2 2 (D) x' + 2 TE dx (F) 1 43 dx (E) dxProblem #3: A gate in an irrigation canal is constructed in the form of a trapezoid 3 m wide at the bottom, 51 m wide at the top, and 2 m high. It is placed vertically in the canal so that the water just covers the gate. Find the hydrostatic force on one side of the gate. Note that your answer should be in Newtons, and use g = 9.8 m/s2. Problem #3:Problem #4: Check which one of the following functions is a solution to the differential equation y" ty =cosx. (A) (sin x + x cos x) (B) (e - cos x) (C) - (sinx - x cosx) (D) ; (e - sin x) (E) (cos x + x sin x) (F) = (e + cosx)Problem # 5: For what two values of r does the function y = e\" satisfy the differential equation y\"+y'42y= 0'? Problem #5 |:| If there is only one value of r then enter it ' twice, separated with a comma (e.g., 12,12)