Begin2.DVI

Sector of Circle Area=^1 2 r^2 θ, θin radians s=arclength=rθ, θin radians Perimeter= 2r+s Rectangular Parallelepiped V =Volume=a ...

Chord Theorem for circle a^2 =x(2R−x) Right Circular Cylinder V =Volume=(Area of base)(height)= (πr^2 )h Lateral surface area= 2 ...

Binomial Expansion Forn= 1, 2 , 3 ,...an integer, then (x+y)n=xn+nxn−^1 y+n(n−1) 2! xn−^2 y^2 +n(n−1)(n−2) 3! xn−^3 y^3 +···+yn ...

Trigonometry Pythagorean identities Using the Pythagorean theoremx^2 +y^2 =r^2 associated with a right triangle with sides x, y ...

Multiple angle formulas sin 5A=5 sinA−20 sin^3 A+ 16 sin^5 A cos 5A=16 cos^5 A−20 cos^3 A+ 5 cosA tan 5A=tan (^5) A−10 tan (^3) ...

Powers of trigonometric functions sin^2 A= 1 2 − 1 2 cos 2A, sin^3 A=^3 4 sinA−^1 4 sin 3A, sin^4 A=^3 8 −^1 2 cos 2A+^1 8 cos 4 ...

Special Numbers Rational Numbers All those numbers having the form p/q, where pand q are integers and q is understood to be diff ...

Greek Alphabet Letter Name A α alpha B β beta Γ γ gamma ∆ δ delta E  epsilon Z ζ zeta H η eta Θ θ theta I ι iota K κ kappa Λ λ ...

Inequalities can be defined in terms of addition or subtraction. For example, one can define a < b if and only ifa−b < 0 a ...

since equals can be added to both sides of an inequality without changing the in- equality sign. Using the fact that both sides ...

Cramer’s Rule The system of two equations in two unknowns α 1 x+β 1 y=γ 1 α 2 x+β 2 y=γ 2 or [ α 1 β 1 α 2 β 2 ] [ x y ] = [ γ 1 ...

Appendix C Table of Integrals Indefinite Integrals General Integration Properties IfdFdx(x)=f(x), then ∫ f(x)dx=F(x) +C If ∫ ...

8. ∫ u′(x)dx u(x) = ln|u(x)|+C 9. ∫ (αu(x) +β)nu′(x)dx=(αu(x) +β) n+1 α(n+ 1) +C 10. ∫ u′(x)v(x)−v′(x)u(x) v^2 (x) dx= u(x) v(x) ...

General Integrals 28. ∫ c u(x)dx=c ∫ u(x)dx 29. ∫ [u(x) +v(x)]dx= ∫ u(x)dx+ ∫ v(x)dx 30. ∫ u(x)u′(x)dx=^12 |u(x)|^2 +C 31. ∫ [u( ...

∫ x^2 Xndx=b^13 [Xn+3 n+ 3− 2 aXn+2 n+ 2 + a^2 Xn+1 n+ 1 ] +C ∫ xn−^1 Xmdx=n+^1 mxnXm+mam+n ∫ xn−^1 Xm−^1 dx ∫ Xm xn ...

∫ dx x^2 X^3 = −b 2 a^2 X− 2 b a^3 X− 1 a^3 x+ 3 b a^4 ln| X x| ∫ x dx Xn = 1 b^2 [ − 1 (n−2)Xn−^2 + a (n−1)Xn−^1 ] +C, ...

∫ Xn x dx= Xn n +a ∫ Xn− 1 x dx Integrals containingX=a+bxandY =α+βx, (b 6 = 0, β 6 = 0, ∆ =aβ−αb 6 = 0 ) ∫ dx XY = 1 ∆l ...

Integrals containing terms of the forma+bxn ∫ dx a+bx^2 =      √^1 ab tan−^1 (√ b ax ) +C, ab > 0 1 2 √ −ab ln ∣ ...

Integrals containingX= 2ax−x^2 , a 6 = 0 ∫ √ X dx=(x− 2 a) √ X+a 2 2 sin − 1 ( x−a |a| ) +C ∫ dx √ X = sin−^1 (x−a |a| ) ...

∫ dx xX= 1 2 cln| x^2 X|− b 2 c ∫ dx X ∫ dx x^2 X= b 2 c^2 ln| X x^2 |− 1 cx+ 2 ac−∆ 2 c^2 ∫ dx X ∫ dx X^2 = bx+ 2c ...