Integral applications pt 2 multiple choice. need help quickly please, will give helpful

If f(a) = 2e3x , what is the average value of f(x) between [1, 4]? O 36,163.268 O 38, 125.341 O 108,501.382 O 109,602.341If an object is moving with v(t) = 3 cos(t) and the position X(0) = 1, what is the position of the object at t = 6? O 0.162 O 0.253 O 0.452 O 0.531\fThe graph shows the velocity v(t) of an object. Calculate the object's displacement between [2, 8]. O 13.5 0 14.5 0 15 O 15.5 If the position of an object is given by s(t) = cot(t) What is the displacement of the object betweent = and t = O 2.577 O 1.577 O 0.577 O -0.577If an object is moving along a horizontal line, such that it's velocity, v(t) = 3 (3t+4) what is the object's displacement between t = 0 and t = 5? O 1.558 O 1.944 O 2.558 O 2.944What is the formula for the total distance traveled by an object with a velocity v(t) = -3t2 + 9 on the interval [0, 5]. o - So (-3+2 + 9) dt + S3 (-3+2 + 9) dt 0 - 10 3 (-3+2 + 9) at + S = (-3+2 + 9) dt o So (-3+2 +9) at - S3 (-3+2 + 9) dt o S 3 (-3+2 + 9) dt - S (-3+2 + 9) dt