Grundkursen i analys, hemuppgifter till vecka 46 1. Beräkna

ws26 u-sub answers.pdf - Humble ISD

+ x2. 2+ x]. 2. 1. = 2π (. 31 Om y = tan x blir y′ = 1 + tan2 x, y′′ = 2 tanx + 2 tan3 x och y′′′ sec2 x = 1 + tan2 x csc2 x = 1 + cot2 x sin (x + y) = sin x · cos y + cos x · sin y dx sin x = cos x d dxcos x = − sin x d dx tan x = sec2 x d dxcot x = − csc2 x d. =-13[x]π/20+43∫π/20sec2x4sec2x-3dx (Divide numerator nad denominator by cos2 x in second integral) =π6+43∫π/20sec2x4(1-tan2x)-3dx.

3. 2. ∫ xn dx = xn+1 n + 1. + C (n ̸= −1).

sin4 x cos x dx = ∫ u4 du ∫ dx = ∫ eu du ∫ 2 dx = ∫ 1 ∫ 2

In calculus, trigonometric substitution is a technique for evaluating integrals. Tan2 X / 1 + Tan2 X Dx; Question: Tan2 X / 1 + Tan2 X Dx. This problem has been solved! See the answer. Evaluate the integral and show your work please!

Calculus Summary

3 [1 − (−1)]. = 2 ln 10. = 2. 3 e u = x2 − 3 ∴ d d u x. = 2x f u = x3 + 1. (x4 + x3 + x + 1) dx. = 2π [ x5.

16.. u u. 16. tan2 X cos3 X dX = sin2 X cos2 X cos3 X dX Þcos3(x)sin4(x)dx Þcos2(x)sin4(x)cos(x)dx u sin(x), du cos(x)dx tan2(x) 1. 4 tan4(x) C. (b) Þtan(x)sec3(x)dx u sec(x),du tan(x)sec(x)dx.
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Find all points on the graph of f(x) at which the tangent line is ho 2009-06-13 tan2(x+y)= dxdy Substituting v =y +x ⇒ dxdv = dxdy +1tan2v − dxdv +1= 0 ⇒ sec2v = dxdv ⇒ cos2vdxdv = 1Integrating both sides w.r.t x∫ cos2vdxdv dx = ∫ dx ∫ 21+cos2v dv =∫ dx ⇒ 41 sin2v + 2v =x+c ⇒ 2(x −y) =c+sin2(x… BITSAT 2007: ( 1+ tan2 x / 1 - tan2 x) dx is equal to (A) log ( 1- tan x/ 1 + tan x) + c (B) log ( 1+ tan x/ 1 - tan x) + c (C) Find ∫ [c o t x + t a n x ] d x Answer ∫ [ cot x + tan x ] d x ⇒ ∫ [ cot x + c o t x 1 ] d x ⇒ ∫ [ c o t x c o t x + 1 ] d x ⇒ ∫ [ tan x ( cot x + 1 ) ] d x L e t tan x = t 2 d i f f . w . r . t . x , S e c 2 x = 2 t d x d t ( 1 + tan 2 x ) = 2 t .

Q: Let: f(x)=2x3−3x2−12x+6. a. Find all points on the graph of f(x) at which the tangent line is ho 2009-06-13 tan2(x+y)= dxdy Substituting v =y +x ⇒ dxdv = dxdy +1tan2v − dxdv +1= 0 ⇒ sec2v = dxdv ⇒ cos2vdxdv = 1Integrating both sides w.r.t x∫ cos2vdxdv dx = ∫ dx ∫ 21+cos2v dv =∫ dx ⇒ 41 sin2v + 2v =x+c ⇒ 2(x −y) =c+sin2(x… BITSAT 2007: ( 1+ tan2 x / 1 - tan2 x) dx is equal to (A) log ( 1- tan x/ 1 + tan x) + c (B) log ( 1+ tan x/ 1 - tan x) + c (C) Find ∫ [c o t x + t a n x ] d x Answer ∫ [ cot x + tan x ] d x ⇒ ∫ [ cot x + c o t x 1 ] d x ⇒ ∫ [ c o t x c o t x + 1 ] d x ⇒ ∫ [ tan x ( cot x + 1 ) ] d x L e t tan x = t 2 d i f f . w .
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p p p p p p p p

|(x+2)/x-2 dx u=X. 2. +.

Primitiva funktioner - Yumpu

u = sin x, du = cos x dx / 4 2 / 2 2 20 0 cos 1 sin 1 x du dx x u = + + 1 2 / 2 0 1 [tan ] 2 tan 2 Definitionsmängd, x ≠ (k + ½)π, k∈ℤ.

= 2 ln 10 − 0.