More about areas 50 2.2. The tables give a nicer or more useful form of the answer than the one that the cas will yield. Csun, integrals, table of integrals, math 280, math 351, differential equations created date:
Integral Table Pdf Integral Table Pdf / 2 / (71) sin ax
2 integration table (integrals) notation:
Table of useful integrals, etc.
A(t)y00+b(t)y0+c(t)y(23) = 0 standard form: X dx= 2 ax+ b+ b xyax+ b' 26. Integration using tables and cas 39 1.9. Second order linear equations general form of the equation general form:
Csun, integrals, table of integrals, math 280, math 351, differential equations created date:
U inverse trig function (sin ,arccos , 1 xxetc) logarithmic functions (log3 ,ln( 1),xx etc) algebraic functions (xx x3,5,1/, etc) trig functions (sin(5 ),tan( ),xxetc) Knowing which function to call u and which to call dv takes some practice. Improper integrals 46 chapter 2. Applications of integration 50 2.1.
Csun, integrals, table of integrals, math 280, math 351, differential equations created date:
Du = du dx dx = u0 dx; The handbook consists of chapters, sections and subsections. For indefinite integrals drop the limits of integration. Table of integrals basic forms z xndx= 1 n+ 1 xn+1 + c (1) z 1 x dx= lnx+ c (2) z udv= uv z vdu (3) z 1 ax+ b dx= 1 a lnjax+ bj+ c (4) integrals of rational functions z 1 (x+ a)2 dx= 1 x+ a + c (5) z (x+ a)ndx= (x+ a)n+1 n+ 1 + c;n6= 1 (6) z x(x+ a)ndx= (x+ a)n+1((n+ 1)x a) (n+ 1)(n+ 2) + c (7) z 1 1 + x2 dx= tan 1 x+ c (8) z 1 a2 + x2 dx= 1 a.
The product of two integrals can be expressed as a double integral:
C, n, and a > 0 are constants The equations within a section are arranged in increasing order of complexity. Table of integrals basic forms z xndx= 1 n+ 1 xn+1 (1) z 1 x dx= lnx (2) z udv= uv z vdu (3) z 1 ax+ b dx= 1 a lnjax+ bj (4) integrals of rational functions z 1 (x+ a)2 dx= 1 x+ a (5) z (x+ a)ndx= (x+ a)n+1 n+ 1 + c;n6= 1 (6) z x(x+ a)ndx= (x+ a)n+1((n+ 1)x a) (n+ 1)(n+ 2) (7) z 1 1 + x2 dx= tan 1 x (8) z 1 a2 + x2 dx= 1 a tan 1 x a (9) z x a 2. Sn+1 (11) tx (x 1 2r) ( x+ 1) sx+1 (12) sinkt k s2 + k2.
Table of basic integrals basic forms z (1) xn dx = z (2) 1 xn+1 , n 6= −1 n+1 1 dx = ln |x| x z z udv = uv
Arc length, parametric curves 57 2.4. What follows is a selection of entries. The substitution u gx= ( )will convert (( )) ( ) ( ) ( ) b gb( ) a ga ∫∫f g x g x dx f u du= using du g x dx= ′( ). Standard integration techniques note that at many schools all but the substitution rule tend to be taught in a calculus ii class.
3 2;cos2 ax (75) z cosaxdx= 1 a sinax (76) z cos2 axdx= x 2 + sin2ax.
U = u(x) is differentiable function of x; Here is a general guide: Integral table = − ∫ ∫ udv uv vdu ∫ & = −∫& ( ) ( ) ( ) ( ) ( ) ( ) f x g x dx f x g x f x g x dx sin( ) ax dx 1 axcos( ) ∫ =− a ax dx 1 axcos( ) sin. Integration by parts 21 1.6.
Equations and formulas are numbered separately in each section.
Y00+p(t)y0+q(t)y= f(t(24) ) the general solution of (22) or (24) is For n even integral 7 can be done by taking derivatives of equation 2 with respect to a. The copyright holder makes no representation about the accuracy, correctness, or If a term in your choice for yp happens to be a solution of the homogeneous ode corresponding to (4), multiply this term by x (or by x 2 if this solution corresponds to a double root of the
E−ax2dx= 1 2 π a # $% & ’(1 2 0 ∞ ∫ ax xe−2dx= 1 2a 0 ∞ ∫ x2e−ax2dx= 1 4a π a # $% & ’(1 2 0 ∞ ∫ x3e−ax2dx= 1 2a2 0 ∞ ∫ x2ne−ax2dx= 1⋅3⋅5⋅⋅⋅(2n−1) 2n+1an π a $ %& ’ 1 2 0 ∞ ∫ x2n+1e−ax2dx= n!
©2005 be shapiro page 3 this document may not be reproduced, posted or published without permission. Integrals with trigonometric functions (71) z sinaxdx= 1 a cosax (72) z sin2 axdx= x 2 sin2ax 4a (73) z sin3 axdx= 3cosax 4a + cos3ax 12a (74) z sinn axdx= 1 a cosax 2f 1 1 2; Integral 4(5) can be done by integrating over a wedge with angle π 4 (−π 4), using cauchy’s theory to relate the integral over the real number to the other side of the wedge, and then using integral 1. F(x) and g(x) are any continuous functions;
Trigonometric integrals and trigonometric substitutions 26 1.7.
The extensive table of contents provides rapid access to the desired equations. 23 ( ) 2 1.
