Finding specific solutions using integration The acceleration of an object at time t is given by a (t) = 12t2 - B. Initially the object is moving at 13 feet per seconds. After 1 second the object has traveled 5 feet. Find the position function s (t) for the object. Find the equation of the curve that goes through the point (2, -8) and whose tangent line has a slope of f'(x) = x3 - 16x + 1. . Evaluating definite integrals (64 ( VX- 7)" dx 40 2vX - dx - 3 (2y+ 1jzdy [ (8x ' + 3 ) (78 + 3xdx Area between curve and the x-axis If / (x) = ex - 1 use calculus to find the area (correct to 2 decimal places) between f (x) and the x-axis from x = -2 tox = 3. Find the area of the region between f (x) = x3 - 4x and the x-axis from x = -Z to x = 4. Area between curves If f (x) = = and g(x) = 5 - x, using calculus, find the area enclosed by f (x) and g(x) (round to 2 decimal places). Find the area of the region bounded by the curves f (x) = x2 - 3x + 12 and f (x) = 18 + x - x 2 Applications with integrals The rate of growth of the length of a new strain of corn can be approximated by L(t) = re"-, where t represents time measured in months. The growth in the second month is 17cm. Find the length function (use one decimal place where appropriate)