Equality Holds - Calculus - Quiz, Exercises of Calculus

This is class quiz. Its from Calculus class. Some key points are: Equality Holds, Table, Space, Definite Integral, Evaluate, Real Numbers, Substitution

Typology: Exercises

2012/2013

Uploaded on 03/16/2013

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Name:
Math 106A: Fall 2011
Quiz 1: September 19
Please write your final answer in the space provided. For full credit you must show your work. Good Luck!
You may or may not find the following table helpful.
f(x)f0(x)
sin xcos x
cos xsin x
tan xsec2x
sec xsec xtan x
1. Find real numbers aand bso that equality holds. (You do NOT need to evaluate the definite integral.)
Z5
3
x(1 + x2)15dx =Zb
a
u15du (1)
2. Use the method of substitution to evaluate the indefinite integral.
Z3x
6x2dx (2)
OVER
pf2

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Name:

Math 106A: Fall 2011

Quiz 1: September 19

Please write your final answer in the space provided. For full credit you must show your work. Good Luck!

You may or may not find the following table helpful.

f (x) f ′(x)

sin x cos x

cos x − sin x

tan x sec^2 x

sec x sec x tan x

  1. Find real numbers a and b so that equality holds. (You do NOT need to evaluate the definite integral.)

3

x(1 + x

2 )

15 dx =

∫ (^) b

a

u

15 du (1)

  1. Use the method of substitution to evaluate the indefinite integral.

3 x

6 − x^2

dx (2)

OVER

  1. Use the method of substitution to evaluate the indefinite integral.

sec^2 x √ 1 − tan^2 x

dx (3)