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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