In this guided problem we consider how to solve some indefinite integrals that involve sin and cos. Note evaluation stops at your first wrong answer. We want to find f f (x)dx. We attempt the substitution x = arctant. In general (if there are no additional restrictions coming from the definition of f), this is a valid substitution for x E (a, b), where a = and b = (Type "pi" to enter ). With this substitution: dx dt 1. = (enter the answer as a function of t). 2. Therefore in the integral dx becomes 3. Any occurrence of sin x becomes 4. Any occurrence of cos x becomes For 3. and 4. enter functions of t. To do this, first consider the identities sin x = Use this to evaluate S sin 1 x cos x -dx. First enter the result as a function of t: You should ignore any integration constant. tan x 1+tan2(x) and cos x = 1 1+tan2(x) Finally express your result as a function of x keeping in mind that t = tan x and t = 1 = cot x: tan x S 1 dx = = sin x cos x dx sin (x) cos(x) is on (0,/2) given as f(x) = (Do the previous problem first. Do not enter any constant of integration.)