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Second opinion] 1) Use series...

Second opinion] 1) Use series to approximate the definite integral to five decimal places. ∫from 0 to 0.5 of (t^2/1+t^4) dt2) Find the Maclaurin series for f(x) using the definition of the Maclaurin series. f(x) = ln(4 − x)3) Find the exact length of the curve. y=2ln(sin(x/2)), pi/6 ≤x≤pi4) Find the area of the surface obtained by rotating the curve about the y-axis. y = (1/4)x^2- (1/2) ln x, 1 ≤ x ≤ 65) The figure shows the vertical sides of a trough that is completely filled with water. Find the force exerted by the water on one end of the trough. (Use 62.4 lb/ft3 for the weight density of water.)<--7ft-->___________---------\ / |\ / 5ftv ---------------|6)Find the centroid of the region bounded by the graphs of the given equations. y = e^3x, y = 0, x = 0, x= 1/37) Find the orthogonal trajectories of the family of curves. y = (x + k)^−88). Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter.

x = cos theta + sin 2 theta + 4, y = sin theta + cos 2 theta + 4, theta = pi9) set up, but do not evaluate, an integral that represents the length of the parametric curve.x=t=t^10, y=(10/9)t^(9⁄8), 8≤t≤18

x = cos theta + sin 2 theta + 4, y = sin theta + cos 2 theta + 4, theta = pi9) set up, but do not evaluate, an integral that represents the length of the parametric curve.x=t=t^10, y=(10/9)t^(9⁄8), 8≤t≤18

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