Pennsylvania State University Limit of A Riemann Sum and The Identity Paper just solve the quiz and send me the answers Calculus I: Canvas Quiz 4 April 22,

Pennsylvania State University Limit of A Riemann Sum and The Identity Paper just solve the quiz and send me the answers Calculus I: Canvas Quiz 4
April 22, 2020
This quiz is worth ten points. Show all work and justify your steps where necessary. No calculators
are allowed.
1. Find L3 for f (x) = x + sin(x) on [0, π]. Give an exact answer. (3 points)
2. Use the limit of a Riemann sum and the identity
n
X
i=
i=1
n(n + 1)
to compute the following
2
definite integral: (2 points)
Z
3
1 − 2x dx
1
3. Use geometry of the graph to compute the following definite integral: (3 points)
Z 6
1
x + 3 dx
2 2
Z
4. Compute
17
2f (x) dx given the following values of integrals below: (2 points)
2
Z
17
Z
5
f (x) dx = 15,
−3
Z
−3
5
f (x) dx = −7
f (x) dx = 5,
2

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