Integral Proficiency

December 5th MATH 251 Fall 2017

Circle your Instructor: Faudree, Williams, Zirbes / 15

Name:

This is a 30 minute quiz. There are 15 problems. Books, notes, calculators or any other aids

are prohibited. Calculators and notes are not allowed. Your answers should be simplified unlessotherwise stated. They should begin y0 = or f 0(x) = or dy/dx =, etc. There is no partial credit. If

you have any questions, please raise your hand.

Circle your final answer.

For each function below, find the definite or indefinite integral.

1.

Z 1

0(1� 15v4 + 16v7)dv

2.

Zcos(3⇡x)dx

3.

Zt2 � 2p

tdt

v-3 UAF Calculus 1

=(v- Egvstoodv8) to

= ( ✓ - 3v5+ 2v8 ) to

= 1 - 3 + 2 - O

÷t÷sinl3t# ✓

= ftt"

- ZE "

2) dt

=2gt%-4t"2€=2ztF-4F+@ ✓

Integral Proficiency

December 5th MATH 251 Fall 2017

4.

Z7x2

2 + x3dx

5.

Z 1

0

6

x2 + 1dx

6.

Zsinx

cos3 xdx

7.

Ze1/x

x2dx

v-3 UAF Calculus 1

¥1314.IE?*=7z1n1u1+C=7z1n12tx3#

✓

= btantxlo'

= 6 ltantl - tanto )

= 6¥=eg ✓

-= - futsdu =±(aosx52tcL

u=osX = - fuidu = Isaf ✓

IIIxe.fi#s+a=z@=fexftx4duu=Yx

- fe "

du

Fit"iYfI. en

= -e"€ ✓

Integral Proficiency

December 5th MATH 251 Fall 2017

8.

Z4xp1� x2

dx

9.

Z 1

0(6 + 10x) dx

10.

Ze�5rdr

11.

Zsec ✓(sec ✓ + tan ✓)d✓

v-3 UAF Calculus 1

in txz

= It /f= du

du= -2xd×|= -2 / it" 2

du

fat =XdX= - 4 u

"2+ C

g= -40€ ✓

= text,o¥o ) Ii= 6 +

Ynfo - lottno )

= cotta ✓

= -5155€ ✓

= / ( Seto + secotanotdtt= tano-seco.LT ✓

Integral Proficiency

December 5th MATH 251 Fall 2017

12.

Z1

(6x� 1)1/3dx

13.

Zlnx dx

xdx

14.

Z ✓p3x+

x

2+

2

x

◆dx

15.

Zsinx sin(cosx)dx

v-3 UAF Calculus 1

in 6× . ,

= £/u' Bda

du=6dק

=

f 23h43 + (

=¥lax-D43@ ✓

B.= fudu

u=m× =£u2+cdu=¥d×|=±dnx)2@/

|=lzm2@ ✓

=/ #rxttzx + 2 ' tx ) dx=Fs}x"2++2.3×2+2mlxltc

=2B⇒X"2+lqx2+2mW-£=2_35x"2+lqx2-2m1Xlt#

✓

noor~ } }l3×7312=92-13×543

= - fsinu du

u=ros×

§= oosu + C 0¥

du= - sinxdx= oos(uosx)tCf ✓