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MATH 1501 (6)
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Midterm

test3_1501_Fall2012.pdf

2 Pages
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School
Georgia Institute of Technology
Department
Mathematics
Course
MATH 1501
Professor
Liu
Semester
Fall

Description
Math 1501 K1-K4 L1-L4 Test 3 Total: 20 points Section: Name: Student Number: Fill in the blanks. Make sure to write down your procedure clearly for problems (7)-(12). (1) Let f(x) be a contiuous function on R. Express the limit as a deﬁnite integral. 1 n→∞ n [f(1/n) + f(2/n) + ··· + f(n/n)] = ( ). (1 point). R R (2) Given that 5f(x) dx = 7, 6 f(x) dx = 11, R5 2 2 6 f(x) dx = ( ). (1 point). (3) Set Z x2 1 F(x) = dt, x 1 + t2 ′ F (1) = ( ). (1 point). (4) Z π 2 |sinx| dx = ( ). − 2 (2 points). ′ p 2 (5) Deﬁne a function F such that F (x) = 1 + sin x and F(π) = 3. F(x) = ( ). (F could contain an integral and you don’t need to evaluate the integral). (1 point).
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