Introduction Numerical integration is a primary tool used by engineers and scientists to obtain approximate answers for definite integrals that cannot be solved analytically. For cxample.since there is no analytic exression for numerical integration must be used to obtain approximate values.The value (5)is the area under the curve )=3/(e-1)for 0t<5 as follow. 6=244s9g92 The purpose of this chapter is to develop the basic principles of numerical integration. Introduction ◼ Numerical integration is a primary tool used by engineers and scientists to obtain approximate answers for definite integrals that cannot be solved analytically. ◼ For example, since there is no analytic expression for , numerical integration must be used to obtain approximate values. The value Φ(5) is the area under the curve y=f(t)=t 3 /(e t -1) for 0≤t≤5 as follow. 3 0 ( ) 1 x t t x dt e  = −  3 5 0 (5) 4.8998922 1 t t dt e  =  −  ◼ The purpose of this chapter is to develop the basic principles of numerical integration