5.2 Integration by SubstitutionMAC2233 (3.4) FIU, MDC-North5.2 Integration by SubstitutionIntegration by substitution is reversing the chain rule for differentiation. Start by defining a u = u(x) that simplifies the integrand. Transform the integral so that all terms involving x and dx to terms involving u and du. The transformed integral will be divided by the derivative of u.Find the indicated integral. Check your answers by differentiation.1.xe dx5� 2.( ) ( )x x dx5 2[ 1 3 1 5]- + - +�3.( )xdxx2235� �� �� �� �+� ��4.x xdxx x34 210 56-- +�5.xdxx2ln�MAC2233 (3.4) FIU, MDC-North6.tdtt11-+�The velocity v(t) = x’(t) at time t of an object moving along the x axis is given, along with the initial position x(0) of the object. Find: [a] the position x(t) at time t; [b] the position of object at time t = 4; and [c] the time when the object is at x = 3:7.( )( )tx tt32 22'1-=+; x(0) =
View Full Document
Unlocking...