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ENG TECH 3MA3 TEST 2
WINTER 2019

Name: ____________________________________________
Student Number: ___________________________________
Total: 36 marks
Duration: 90 min.
The test is closed book.
FORMULA SHEET


= 0 where c is a constant


() = −1


=


() =


=
1
ln



ln =
1




( ) =


( ) = − ∙


( ) = −


( ) = ∙


( ) = 2


( ) = −2

∫ =
+1
+ 1
+ , ≠ −1 ∫
1
+
=
1

ln| + | +
∫ + =
1

+ + ∫ sin( + ) = −
1

cos( + ) +
∫ cos( + ) =
1

sin( + ) + ∫ sec2( + ) =
1

tan( + ) +
∫ csc2( + ) = −
1

cot( + ) + ∫ sec( + ) tan( + ) =
1

sec( + ) +
∫ tan( + ) =
1

ln|sec( + )| + ∫ csc( + ) cot( + ) = −
1

csc( + ) +
∫ cot( + ) =
1

ln|sin( + )| + ∫
1
2 + 2
=
1

tan−1 (


) +
∫ sec( + ) =
1

ln|sec( + ) + tan( + )| +
∫ csc( + ) =
1

ln|csc( + ) − cot( + )| +
Trigonometric Identities
sin2 + cos2 = 1 sin 2 = 2 sin cos sin sin =
1
2
[cos( − ) − cos( + )]
tan2 + 1 = sec2 cos 2 = cos2 − sin2 cos cos =
1
2
[cos( − ) + cos( + )]
1 + cot2 = csc2 cos 2 = 1 − 2 sin2 sin cos =
1
2
[sin( + ) + sin( − )]
cos 2 = 2 cos2 − 1

1a /6
1b /6
1c /6
1d /6
1e /6
1f /6
Total /36

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1. Evaluate the following integrals.
a)∫
+1
√4
3
2
1
[6 marks]

b)∫

(+1)10
[6 marks]


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c) ∫ cos2 [6 marks]

d) ∫
3+1
2+2
[6 marks]

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e) ∫
1
3−22+
[6 marks]

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f) ∫ cos ln(sin ) [6 marks]









































































































































































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