Rutgers University Calculus Zoom Proctored Final Exam thank you for taking on my assignment on such a busy time for you.Please do it as the same format you

Rutgers University Calculus Zoom Proctored Final Exam thank you for taking on my assignment on such a busy time for you.Please do it as the same format you did last time because I have to right then on paper. If you can please get it done by 6 it’ll be amazing. And just like last time if you would like you can watch videos and get an idea. Name: ___________________
Prof. Yeung
Zoom Proctored Final Exam
Date: ____________________
MA 120 Summer 2020
Direction: Please show all your work for each of the following problems in order to receive full credits.
1. Use a simple area formula from geometry to find the area under function ??(??) that gives the area
between the function ??(??) = 5?? ? 8 and the interval [??, ??] = [?2, ??] (12 points)
2. Evaluate the following integral: (15 points)
??+5
a) ? 5 ????
???
b) ?(?? + 2)??? ????
3
c) ? (?? + 2 ) ????
Cos ??
3. Evaluate the integrals using appropriate substitutions. (18 points)
8
a) ? ?? 7 ??? 8 ? 2 ????
??
b) ? 2 ????
?4?? +2
c) ? tan7 7?? sec 2 7?? ????
4. Applying sigma notation and related theorem: (12 points)
a) Evaluate
??
?? 2 1 2
?( ) ( )
??
??
??=1
b) Evaluate
??
? (5 +
??=1
9?? 1
)
?? ??
5. Given ??(??) = ?3 + ?? + 4. Use the definition of 4.4.3 to evaluate each of the area in the range [0, 6] if
?? = 4. (18 points)
a) Find the area under the curve when ????? is the left endpoint of the subinterval.
b) Find the area under the curve when ????? is the midpoints of the subinterval.
c) Find the area under the curve when ????? is the right endpoint of the subinterval.
6. Evaluate the integrals using the Fundamental Theorem of Calculus and (if necessary) properties of the
definite integral. (18 points)
4
??2,
??>2
a) ??1 ??(??) ???? if ??(??) = {
2 ? ??, ?? ? 2
1
??
b) ?04 (?? + 9sec 2 ??) ????
2?? ??
c) ???
8
sin ?? ????
7. Find all value of ?? ? in the stated interval that satisfy the Mean-Value Theorem for Integrals (4.6.2).
??
Given ??(??) = 8 sin ??; [??, 2??]. Hint: Use your answer from question # 6 part c) to help you satisfy
4.6.2 Therorem. (7 points)
2

Purchase answer to see full
attachment