4. It is given that the mixed second derivative of z is given by z (let the constants of integration be zero). 2 - (1/) = a + m x dx dy 2 a + [mx] Step 2: Integrate your result from Step 1 with regards to y (x is a constant) Step 1: Integrate with regards to x (y is a constant) What was the expression for [10] 5. Calculate the integral sin" (1) cos( t)dt. Your solution will be an expression in terms of m. Will this expression hold (won't result in division by zero) for m = _ and m = -1 ? [10] 6. Determine the volume V of the 3 dimensional lampshade formed (see diagram below) by rotating the 2 1 between x = 2a and x = 4a about the x axes if V = dimensional curve y = (x-a) x Hint: At a certain point of your calculation, you might need to substitute x=0, x= a and x = 2a Aa y dx. [10]