Weekly Tutorial 5 for Math. 69.107A,
Elementary Calculus I

Instructor: Dr. Angelo Mingarelli

Notes: These are group tutorials; each question is to be divided among the group (at most 5 students in a given group), solved and submitted to the T.A. at the end of the 50 min. period. NOTES ALLOWED, along with group interaction...All students within a group will be assigned the same grade for this tutorial...
This online test is meant to be printed and handed in.
Solutions will appear later on during the term ...

Group names (Please PRINT) & Student Numbers:







1. Evaluate the definite integral of the function f(x) = eCubeRoot(x) x-2/3 over the x-interval ranging from 1 to 8.

a) None of these
b) e2 - e
c) 3( e2 - e)
d) 3e2

2. Evaluate the indefinite integral of the function cos(2t)/sqrt(1 + sin(2t)).

a) ln|1 + sin(2t)| + C
b) sqrt(1 + sin(2t))
c) sqrt(1 + cos(2t))/2
d) sqrt(1+ sin(2t)) + C

3. Evaluate the indefinite integral of the function ln(2 sqrt(x))/x.

a) ln(2t) + C
b) ln(2sqrt(t)) + C
c) ln(2 sqrt(t))2
d) None of these

4. Use Simpson's Rule with n = 4 in order to approximate the value of the definite integral of the function e1/x over the interval [1,2] to six decimal places.

a) 2.200651
b) 2.017234
c) 2.032147
d) None of these

5. Evaluate the derivative of the function defined by the integral of e-t2 over the variable range from sqrt(x) to sin(x).

a) e-sin2(x) - e-x + C
b) e-cos2(x) sin(x) - e-x/(2 sqrt(x))
c) e-sin2(x) cos(x) - e-x/(2 sqrt(x))
d) 2 (e-sin2(x) - e-x) sqrt(x)

6.Evaluate the definite integral of the function tan(u) between the limits 0 and Pi/4.

a) ln(2)
b) ln(2) / 2
c) ln(2) + C
d) None of these

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