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Graph the function f(x) over the given interval. Partition the interval into 4 subintervals of equal length. Then add to your sketch the rectangles associated with the Riemann sum , using the indicated point in the kth subinterval for ck.f(x) = x2 – 2, [0, 8], midpoint

Solve the initial value problem. = 9 sin 2 x cos x, y(0) = 3

Find a formula for the Riemann sum obtained by dividing the interval [a, b] into n equal subintervals and using the right-hand endpoint for each ck. Then take a limit of these sums as  to calculate the area under the curve over f(x) = 9x + 8 over the interval [0, 3].

Find the total area of the region between the curve and the x-axis.y = 2x – x2; 0 ≤ x ≤ 2

Solve the initial value problem. = e7x cos e7x, y(0) = 0

Find the total area of the region between the curve and the x-axis.y = 2x – x2; 0 ≤ x ≤ 2

Find the area of the shaded region.y = -x4

Graph the function f(x) over the given interval. Partition the interval into 4 subintervals of equal length. Then add to your sketch the rectangles associated with the Riemann sum , using the indicated point in the kth subinterval for ck.f(x) = -2×2, [0, 4], left-hand endpoint

Evaluate the integral. dx

Find the area of the shaded region.y = -x4