Learning Guide Learning Guide

68 • Chapter 3: Finding Solutionscos(a x) cos(a x) + a x sin(a x)− + + b x 2aa> simplify(%);x (sin(a x) + b x)It is unnecessary to use the inert forms Diff and Int in conjunctionwith the value command to symbolically compute the derivative andintegral, respectively. The results can be calculated in single commandsby using diff and int, respectively.You can also perform definite integrations. For example, recomputethe previous integral on the interval x = 1 to x = 2.> Int(df,x=1..2);∫ 21sin(a x) + x cos(a x) a + 2 b x dx> value(%);2 sin(2 a) + 3 b − sin(a)Consider a more complicated integral.> Int(exp(-x^2), x);∫e (−x2) dx> value(%);1 √ π erf(x)2If Maple cannot clearly determine whether a variable is real or complex,it may return an unexpected result.> g := t -> exp(-a*t)*ln(t);g := t → e (−a t) ln(t)