5.5 Exceeds If f is continuous for all x, which of the following integrals have the same value? a) Saf(x )ax b)so f ( x + a ) dx c) late f (x + c ) dx 7.1 Exceeds The acceleration a of an object in rectilinear motion is given by a(t) = the-t ft/s2. a) Find the velocity v of the object if the initial velocity is v(0) = 5 ft/s. b) Find the position s of the object if the initial position is s(0) = Oft. 7.2 Exceeds a) What is wrong with the following? cost x dx = (cos x)3 cos x dx = (cos2x)3/2 cos x dx = (1 - sin x)3/2 cos x dx = (1-u2)3/2du = 0 b) Find So costx dx. 7.3 Exceeds Use a trigonometric substitution to derive each formula. a) S dx XVx2 -az -sec-12 + C b) S : dx Vx 2 + a 2 = In x + vx2 + az|+ c 7.4 Exceeds Use the partial fraction decomposition method to find S dx 1+x4. Hint: Factor 1 + x into irreducible quadratics