MATH 205 Fall 2019 - webwork assign 2 PDF

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Hussein Olleik

C

WeBWorK assignment due : 09/27/2019 at 11:59pm EDT. 5. (1 point) Evaluate the definite integral:

1. (1 point) Given f (t) =

Z t 2 x + 9x + 18 0

1 + cos2 (x)

Z −4  −1  x + 2x dx =

dx

−8

At what value of t does the local max of f (t) occur? t=

Answer(s) submitted: • ln(0.5)-48

Answer(s) submitted:

(correct)

• -6

6. (1 point) Evaluate the definite integral. Z 3 2 3x + 2 dx = x2 1

(correct) 2. (1 point) Find the derivative of g(x) =

Z 4x u+5 5x

u−2

Answer(s) submitted: • 22/3

du

(correct)

7. (1 point) Evaluate the integral

g′ (x) = HINT: Z 4x u+5 5x

u−2

du =

Z 4x u+5 0

u−2

du +

Z 0 u+5 5x

u−2

Z 5

(7ex + 9 cos(x)) dx

0

du

Integral = Answer(s) submitted: • 7eˆ5+9sin(5)-7

Answer(s) submitted: • (4(4x+5)/(4x-2))-(5(5x+5)/(5x-2))

(correct)

(correct)

8. (1 point) Find a function f and a number a such that

3. (1 point) The Fundamental Theorem of Calculus. Use the Fundamental Theorem of Calculus to find the derivative of 14 Z x2  1 2 f (x) = t − 1 dt 3 3

1+

Z x f (t)

t5

a

dt = 6x−2

f (x) = a= Answer(s) submitted: • -12xˆ2 • sqrt6

f ′ (x) =

(correct) Answer(s) submitted:

9. (1 point) Use the Fundamental Theorem of Calculus to find the derivative of Z sinx   cos t 2 + t dt. F(x) =

• 2x(xˆ4/3-1)ˆ14

(correct) 4. (1 the following antiderivatives: Z point)   Calculate +C. (a) x 8 + x5 dx = (b) (c)

Z

−5x5 + 13x6

dx = x−3  2 2 + x4 dx =

Z 

−2

F ′ (x) =

Answer(s) submitted: • (cos(sinxˆ2)+sinx)cosx

+C.

(correct)

10. (1 point) Evaluate the integral

+C.

Answer(s) submitted:

Z 9 −9x − 10

• xˆ7/7+4xˆ2 • -5xˆ9/9+13xˆ10/10 • 4x+xˆ9/9+4xˆ5/5

1

Integral =

(correct) 1

Answer(s) submitted: • -196

(correct)

√ x

dx

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