Question

please help me solve these two questions. I have done the first and just trying to check my answer and im kinda lost on the second

- Joker2+1) (b) Calculate the derivative of pin(2) F(x) = e' Vidt, and determine whether F(x) is increasing or decreasing at the point x = 1. 2. Find the antiderivative F(x) of f(x) sin(x) + V1 + 2 tan(x) cos2(x) such that F(0) = 0.

Answer 1

page 1

C087 Given St² +44 I dt fan 163929-1 We know that f212) glidt da f11292 foto, glidt ef family faiso = 3 (fil21fi'ca then coga dy de 124 tt i at dt tenil(3012) - 1 V2 = (le cos2+3) ?+Le +3) ?+ le cost+3 ) + 1) +3)+1) *** de ce comm+3) – ((tan)(3x?)_112 + Hand(332) –1 +1)* g (to 323 -12 +9+6ecoste C091 4127-sina e ecosy, -6649n+(372)]2+1-2 ton '48x2) - fant(33rjj 3 1+9574 2002 63 a do dy da CO2 2002 CORY tre +13) 6x 1 +934 (19n"1322)2-3 tan! (332) +1)

page 2

2 for = Sin(X) + 1+2109x сол2 х. sina Сол-yt +1+2.00 22. cos2x tange, secge + gece [ +21003 then I feoda a Jaanz-Seck + sec?x{1+ 230DX ) dx Szonde gecx dx + f seeloc s 1+ 2-4anse dae FO first we have to solve I see220 11t2t0mx de, 1+2 tonnes 2 sec ² x dx. 4312 then f ser?a/14 24062. fut du 2 2 3/2 3/2 312 ㅗ 3 ! (1+2+902) 3. te then from equation 3/2 A2 = secae tý (1+2.10021 Since Flo=0 then 3 1312 to 0 = Sectol +(1+2.dom103) 0 = 1 + $te per 443 then 9/2 F(X) = secar + (1+2.4003) 3