Please help me with the following questions.

1.

Use finite approximations to estimate the area under the graph of the function f(x) = 15 -x-2x between x = - 5 and x = 3 for each of the following cases. a. Using a lower sum with two rectangles of equal width b. Using a lower sum with four rectangles of equal width c. Using an upper sum with two rectangles of equal width d. Using an upper sum with four rectangles of equal width a. The area under the graph of f(x) using a lower sum with two rectangles of equal width is (Type an integer or a decimal.)Using rectangles whose height is given by the value of the function at the midpoint of the rectangle's base, estimate the area under the graph using first two and then four rectangles. f(x) = x2 between x = 2 and x = 3 . . . Using two rectangles to estimate, the area under f(x) is approximately (Type an integer or a simplified fraction.)For the function given below, find a formula for the Riemann sum obtained by dividing the interval [0,5] into n equal subintervals and using the right-hand endpoint for each CK. Then take a limit of this sum as n - co to calculate the area under the curve over [0,5]. f (x ) = x2 + 4 Write a formula for a Riemann sum for the function f(x) = x + 4 over the interval [0,5]. Sn= (Type an expression using n as the variable.)Find the total area of the region between the x-axis and the graph of y = - x - 3x, - 8 Ex = 2 The total area of the region between the x-axis and the graph of y = - x - 3x, - 8 =x = 2 is (Simplify your answer.)Find the shaded region in the graph. The area of the shaded region is (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Type an exact answer in terms of it.) X = 3 y = 2 y = cos x + 1 X It 3 2TC/\fSolve the following initial value problem. d' s = - 36cos(6t + n), s'(0) = 600, s(0) = 0 at 2 S= (Type an exact answer, using it as needed.)