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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

Use a finite approximation to estimate the area under the graph of the given function on the stated interval as instructed.f(x) = x2 between x = 3 and x = 7 using an upper sum with four rectangles of equal width.

Evaluate the integral. dt

Find the area of the shaded region. f(x) = x3 + x2 – 6x