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