Problem 2. igonmetric substitution is a valued technique of integration be- cause it can often transform expressions involving quadratic terms into more manageable trigonometric integrals which we have more tools for. More generally, if f f(a:)da: is an integral, then an inverse subtitution is a substitution of the form a: = g(t) where t is some variable we introduce. If 5'5 = .9\"): then do; = g"(t)dt and so: / mm = / f(9(t)) - grim. b Mgonometric substitution is the special case where a" = E sin 6', 31:51:16,351366 depending on the context. a Explain and demonstrate how to evaluate Jda: usin the inverse sub- 1+ 9 stitution a: = us. Hint: You may use the fact that s u s 4 2 1 = 1 1+u2 u n+u +1+u2 if you nd it useful. (b) Explain and demonstrate how to evaluate f TIE-7'15\"" by using an inverse substitution of the from a: = u\" for some suitable choice of real number a