Understanding Engineering Mathematics

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9.1 Review

9.1.1 Definition of integration ➤253 280➤➤


A.Differentiate


(i) x^3 (ii) sin 2x (iii) 2e^3 x

B. Find the integral of


(i) 3x^2 (ii) cos 2x (iii) 2e^3 x

9.1.2 Standard integrals ➤255 281➤➤


A.Integrate the following functions (include integration constants)


(i) 3 (ii)

2
x^2

(iii)


x (iv) x

1
3

B. Give the integrals of


(i) sinx (ii) ex (iii)

1
x

9.1.3 Addition of integrals ➤257 281➤➤


Integrate 2x^2 +


3
x^2

+ 4


x− 2 ex+4sinx.

9.1.4 Simplifying the integrand ➤258 281➤➤


Find


(i)


dx
cos 2x+2sin^2 x

(ii)


xe2lnxdx

(iii)


(cos 2xsin 3x−cos 3xsin 2x)dx

Hint: think about what you are integrating!


9.1.5 Linear substitution in integration ➤260 282➤➤


Integrate


(i)

1
x− 1

(ii) cos( 3 x+ 2 ) (iii) e^2 x−^1
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