9.1 Review
9.1.1 Definition of integration ➤253 280➤➤
A.Differentiate
(i) x^3 (ii) sin 2x (iii) 2e^3 xB. Find the integral of
(i) 3x^2 (ii) cos 2x (iii) 2e^3 x9.1.2 Standard integrals ➤255 281➤➤
A.Integrate the following functions (include integration constants)
(i) 3 (ii)2
x^2(iii)√
x (iv) x1
3B. Give the integrals of
(i) sinx (ii) ex (iii)1
x9.1.3 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)dxHint: 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