View an example | All parts showing X Suppose that in a memory experiment the rate of memorizing is given by M'(t) = - 0.012t + 0.8t where M'(t) is the memory rate, in words per minute. How many words are memorized in the first 60 min (from t = 0 to t = 60)? If M'(t) is the memory rate in words per minute, then M(t) is the number of words memorized at time t. To find how many words are memorized in the given time length, use the fundamental theorem of integral calculus. [ f( x) dx = F(b ) - F(a) In order to calculate the number of words memorized in 60 minutes, integrate to find M(60). The upper limit of integration is 60. Thus, the value of M(60) can be found using the integral below. 60 60 M(60) = [ M'()at = ] (-0.012+2 +0.8t) dt To solve the definite integral, first find the antiderivative. 60 J (-0.01212 + 0.81) dt = [- 0.00413 + 0.412]% Substitute in the the upper and lower limits. [- 0.00413 + 0.412] % = - 0.004(60)3 + 0.4(60)2 - (-0.004(0)3 + 0.4(0)2) Simplify. - 0.004(60) + 0.4(60)2 - 0 = 576 Therefore, in the first 60 minutes 576 words are memorized.Suppose that in a memory experiment the rate of memorizing is given by M' (t) = - 0.00312 + 0.6t where M'(t) is the memory rate, in words per minute. How many words are memorized in the first 10 min (from t = 0 to t = 10)? In the first 10 minutes words are memorized