Question: Plz answer all Solve the following equation for 0 S x S sin(x) = cos(2x) X = Evaluate the integral and interpret it as the

Plz answer all

Solve the following equation for 0 S x S sin(x) = cos(2x) X = Evaluate the integral and interpret it as the area of a region. * / 2 |4 sin(x) - 4 cos(2x)| dx Sketch the region. Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. 3x = y2, x = 0, y = 5; about the y-axis Sketch the region. Suppose that 4 3 of work is needed to stretch a spring from its natural length of 32 cm to a length of 50 cm. (a) How much work (in J) is needed to stretch the spring from 40 cm to 48 cm? (Round your answer to two decimal places.) (b) How far beyond its natural length (in cm) will a force of 10 N keep the spring stretched? (Round your answer one decimal place.) cm

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