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The questions from test 3 of math 220 (sections al1 and bl1) held in spring 2010. The test covers various topics in calculus, including finding formulas for functions, evaluating limits, definite integrals, and indefinite integrals.
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MATH 220 (sections AL1 and BL1) Test 3 Spring 2010
nlim→∞
∑^ n
k=
( 5 k n^3
n
)
∫ (^6)
2
et
2 dt can be written as a limit. Fill in the missing information in this limit.
∫ (^6)
2
et
2 dt = lim n→∞
∑^ n
k=
[ ]
on the interval [− 5 , 5]. Given that
∫ (^5)
0
f (x) dx = 8 and
∫ (^5)
0
g(x) dx = 3, evaluate the following definite integrals.
(a)
∫ (^0)
5
g(x) dx
(b)
∫ (^5)
5
f (x) dx
(c)
∫ (^5)
− 5
(2f (x) + 4g(x)) dx
(d)
∫ (^5)
− 5
( 4 + (f (x))^3
) dx
(a)
∫ x^2 (x + 4)^10 dx
(b)
∫ sec^6 x tan^3 x dx
x
y
(a) The area of R.
(b) The volume of the solid obtained when R is revolved around the y-axis.
(c) The volume of the solid obtained when R is revolved around the horizontal line y = −10.
