Lecture Review Diff and Int

MAT138 Engineering Mathematics III Review of Derivatives and Integrals Foundational working tools in calculus, the derivative and integral permeate all aspects of modeling nature in the physical sciences. DIFFERENTIATION: It is the procedure of finding derivatives. Derivative of a function is the slope of a curve at any given point. INTEGRATION: It is the reverse of differentiation and it calculates the area under the curve. Derivatives Integrals 1. d [kx] 1.  kdx dx 2. d [ xn 1 ] 2.  xndx dx n 1 1

MAT138 Engineering Mathematics III Derivatives Integrals 3. d [ x5  cos 2x  10] 3. [x4  2sin 2x]dx dx 5 4. d [e4 x  tan 3x  6] 4. [4e4x  3sec2 3x]dx dx 5. d [ x ln( x)] 5. [1 ln(x)]dx dx 2

MAT138 Engineering Mathematics III Derivatives Integrals 6. d [ x 2 sinx] 6. [x2 cos x  2x sin x]dx dx 3

MAT138 Engineering Mathematics III Derivatives Integrals 7. d ( x 2  3x)5 7. 5(x2  3x)4 (2x  3)dx dx 8. d ( 4  2  8) 8. ( 4  4 )dx dx x x2 x2 x3 9. d [x 6  3x 4  2x3  x  54] 9. [6x5  12x3  6x2  1]dx dx 4

MAT138 Engineering Mathematics III Derivatives Integrals 10. d [x3e x ] 10. [x3e x  3x2e x ]dx dx 5

MAT138 Engineering Mathematics III Derivatives Integrals 11. d [ln(2x)  e 2x ] 11. [ 1  2e2x ]dx dx x 6