Download Algebra Integrals Integration Notes and more Study notes Mathematics in PDF only on Docsity!
INDEFINITE INTEGRATION INDEFINITE INTEGRATION Integration is the inverse process of differentiation. That 3. k f (x)dx =k] f(x)dx , where k stant is, the process of finding a function, whose differential J fe) J Foo Mwhere © 18 any constant coefficient is known, is called integration. 4. IEF (x). £(%)..A(8). ... (finite in number) are functions If the differential coefficient of F(x) is f (x), of x, then ie. 2 [F%)] = f(x), then we say that the antiderivative JUU@+ hW+
[email protected] or integral of f(x) is F(x), written as J J (x)dx = F(x), 7 i (aes [fe des If (dee 5. If[ f(x)dx = F(x) +e Here fax is the notation of integration f (x) is the ! integrand, x is the variable of integration and dx denotes 1 “ oo then f f(ax+b)dx =—F(axtb)+e the integration with respect to x. a 1. INDEFINITE INTEGRAL 1.2 Standard Formulae of Integration The following results are a direct consequence of the pd We know that it [F()] = f(x). then | (x)dx = F(x). definition of an integral. Also, for any arbitrary constant C, 1 Jxtdx = xt +C.n#-l. ° n+l” Atr09+cl= 2 Fe0]+0= foo. 2, fodx=log|x|+C x om J feoax =F(x)+C, 5. * dx =e +C This shows that F(x) and F(x) + C are both integrals of the 3 J ° oF same function f(x). Thus, for different values of C, we obtain a different integrals of f(x). This implies that the integral of 4. J at dx= f(x) is not definite. By virtue of this property F(x) is called . log.a the indefinite integral of f(x). +C. 5. Jsinxdx =-cosx+C 1.1 Properties of Indefinite Integration| d 6. Joosxdx =sinx +C 1. ral J f(x)dx | =f) 7. fsec? xdx = tanx+C 2 [feoax=[E[foolde= foo +e 8 feosec’xdx = -cot +
